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Connectivity

Connectivity refers to the degree and manner in which elements within a system—such as nodes, devices, or organisms—are linked or able to interact, enabling the exchange of information, resources, or influences across the structure.^[1] This concept is foundational across multiple disciplines, where it quantifies the structured relationships between spatially or temporally distinct components, influencing system resilience, efficiency, and dynamics.^[2] In essence, connectivity describes both the existence and quality of these linkages, from simple pairwise connections to complex, multi-scale networks that underpin real-world phenomena. In technology and communications, connectivity primarily denotes the capability of devices, systems, or networks to establish secure and reliable links for data transmission, often via wired (e.g., fiber optics) or wireless (e.g., 5G, Wi-Fi) infrastructures.^[3] It encompasses digital networks including mobile broadband, fixed-line internet, satellites, and undersea cables, which collectively support global information flow and enable applications like the Internet of Things (IoT) and cloud computing.^[4] High-quality connectivity ensures low latency, high bandwidth, and minimal disruptions, driving economic growth by connecting businesses, services, and communities worldwide.^[5] In mathematics, connectivity appears in graph theory and topology. In graph theory, it measures the robustness of a graph—the minimal number of vertices or edges whose removal disconnects the graph into multiple components.^[6] A graph is connected if there exists a path between every pair of vertices; otherwise, it consists of disconnected components.^[7] This vertex connectivity (κ(G)) or edge connectivity (λ(G)) is crucial for analyzing network reliability, with applications in computer science for optimizing routing algorithms and in transportation for designing efficient infrastructures.^[8] In topology, connectivity refers to properties of spaces that cannot be divided into disjoint non-empty open sets, such as connected and path-connected spaces, fundamental to understanding continuity and separation in geometric structures. In physics, connectivity is explored through percolation theory, which models the formation of connected clusters in random media leading to phase transitions, and in quantum systems, where entanglement establishes non-local connections between particles.^[9] In biology and ecology, connectivity pertains to the interactions and pathways that allow movement, gene flow, or resource transfer among populations or habitats, sustaining biodiversity and ecosystem health.^[10] In neuroscience, it involves the structural and functional links between brain regions, analyzed to understand information processing and disorders like schizophrenia.^[11] Ecological connectivity maintains lateral (e.g., river-floodplain links), longitudinal (upstream-downstream), and vertical (surface-subsurface) pathways for species migration and hydrological processes, with fragmentation posing threats to resilience.^[12] Across these fields, disruptions in connectivity can propagate vulnerabilities, while enhancements foster adaptability and innovation.

Mathematics

Graph Theory

In graph theory, a fundamental concept of connectivity is that of a connected graph, defined as an undirected graph in which there exists a path between every pair of distinct vertices.^[13] This property ensures that the graph forms a single cohesive structure without isolated parts, distinguishing it from disconnected graphs that consist of multiple separate pieces. The absence of paths between some vertices implies disconnection, highlighting connectivity as a measure of linkage in discrete structures.^[14] Connected components represent the building blocks of any graph, defined as the maximal induced subgraphs that are themselves connected.^[14] In a disconnected graph, these components partition the vertex set, and their identification is crucial for analyzing overall structure. Algorithms such as depth-first search (DFS) or breadth-first search (BFS) efficiently compute connected components by exploring the graph from an arbitrary starting vertex and marking all reachable vertices, repeating the process for unvisited vertices until all are covered; both run in linear time relative to the number of vertices and edges.^[15] A more refined measure is k-connectivity, where the vertex connectivity κ(G) of a connected graph G is the size of the smallest vertex cut—a set of vertices whose removal disconnects G.^[16] A graph is k-vertex-connected if κ(G) ≥ k (for |V(G)| > k), meaning at least k vertices must be removed to disconnect it. Similarly, edge connectivity λ(G) is the size of the smallest edge cut, with a graph being k-edge-connected if λ(G) ≥ k. Menger's theorem (1927) provides a path-based characterization: the minimum size of an A–B vertex separator equals the maximum number of internally vertex-disjoint paths from a non-empty disjoint pair of sets A and B, implying that a graph is k-vertex-connected if and only if every pair of vertices is joined by k internally vertex-disjoint paths.^[17] ^[14] Illustrative examples underscore these concepts. The complete graph K_n on n vertices is (n-1)-connected, as removing fewer than n-1 vertices leaves it connected, with direct edges ensuring maximal linkage.^[18] In contrast, a tree—a connected acyclic graph—is 1-vertex-connected and 1-edge-connected, containing bridges (edges whose removal increases the number of components) and cut vertices (also called articulation points, vertices whose removal increases the number of components).^[19] ^[20] For instance, in a path graph, every non-end vertex is a cut vertex, and every edge is a bridge.^[14] Connectivity principles find application in optimization problems, such as constructing a minimum spanning tree (MST), which connects all vertices of a weighted connected graph with minimum total edge weight while avoiding cycles. Kruskal's algorithm (1956) achieves this by sorting edges by weight and greedily adding the smallest non-cycle-forming edge using union-find for efficiency. Prim's algorithm (1957) builds the MST incrementally from an arbitrary vertex, repeatedly selecting the minimum-weight edge connecting the growing tree to an unvisited vertex. These methods rely on the graph's connectivity to ensure a spanning tree exists, with bridges often included in any MST.^[14]

Topology

In topology, a topological space X is defined as connected if it cannot be partitioned into two disjoint non-empty open sets whose union is X.^[21] This property ensures that the space lacks any "separation" into independent pieces, distinguishing it from disconnected spaces such as the union of two isolated points with the discrete topology, where each point forms a separate open set.^[22] Euclidean spaces \mathbb{R}^n exemplify connected spaces, as any attempt to separate them into disjoint open sets fails due to their inherent continuity.^[22] Path-connectedness provides a stricter criterion for connectivity: a space X is path-connected if, for any two points x, y \in X, there exists a continuous path \gamma: [0,1] \to X with \gamma(0) = x and \gamma(1) = y.^[22] Every path-connected space is connected, since a path would link points across any purported separation, but the reverse does not hold.^[23] The topologist's sine curve, defined as S = \{(x, \sin(1/x)) \mid 0 < x \leq 1\} \cup (\{0\} \times [-1,1]) in \mathbb{R}^2 with the subspace topology, illustrates this distinction: it is connected because any open sets covering the oscillating graph and vertical segment must overlap near the origin, yet it is not path-connected, as no continuous path can traverse from a point on the vertical segment \{0\} \times [-1,1] to a point on the graph due to the unbounded variation in the oscillations approaching x=0.^[23] Local connectedness refines these ideas by requiring that every point in X has a basis of connected open neighborhoods.^[24] In locally connected spaces, the connected components—maximal connected subsets containing a given point—are both closed and open, partitioning X into clopen subsets.^[25] Quasi-components, defined as the intersection of all clopen subsets containing a point, coincide with these components in locally connected spaces, ensuring a clean decomposition.^[25] For instance, \mathbb{R}^n is locally connected, with its sole connected component being the entire space, whereas the subspace of rational numbers in \mathbb{R} has singleton quasi-components that are closed but not open, highlighting the absence of local connectedness.^[24] Higher-dimensional connectivity extends these concepts via algebraic topology, using homotopy groups to probe "holes" in spaces. A space X is n-connected if it is path-connected and its homotopy groups \pi_k(X) = 0 for all $1 \leq k \leq n, meaning maps from lower-dimensional spheres into X are null-homotopic.^[22] Simply connected spaces, which are 1-connected, have trivial fundamental group \pi_1(X) = 0, implying every closed loop contracts to a point; examples include \mathbb{R}^n for n \geq 2 and spheres S^n for n \geq 2.^[22] These notions underpin algebraic invariants like homology, where the 0th homology group H_0(X) \cong \mathbb{Z} for path-connected X, and play a central role in classifying spaces up to homotopy equivalence.^[22] This continuous framework builds on discrete graph connectivity as a combinatorial precursor.^[22]

Computing and Information Technology

Computer Networks

In computer networks, connectivity refers to the ability of devices to communicate and exchange data reliably across interconnected systems. Network topologies define the physical or logical arrangement of these devices and links, directly influencing connectivity characteristics such as redundancy, scalability, and vulnerability to failures. Common topologies include the star, where all nodes connect to a central hub or switch, providing efficient centralized management but introducing a single point of failure if the hub malfunctions; the mesh, in which devices are interconnected with multiple paths for high redundancy and fault tolerance, though at the cost of increased cabling and complexity; and the bus, utilizing a single shared communication line for all nodes, which is simple and cost-effective for small networks but prone to collisions and total failure if the backbone cable breaks.^[26] Protocols ensure reliable end-to-end connectivity by standardizing data transmission rules. The TCP/IP protocol stack, foundational to modern networking, operates across layers to handle packet routing, error detection, and connection establishment. At the transport layer, TCP uses a three-way handshake—SYN, SYN-ACK, and ACK segments—to verify mutual reachability and synchronize sequence numbers before data transfer begins, mitigating issues like packet loss in unreliable networks.^[27]^[28] Network design often employs graph theory models to optimize these topologies for minimal latency and maximal throughput. Key metrics evaluating connectivity include bandwidth, which measures data transfer capacity in bits per second; latency, the delay in packet propagation often measured in milliseconds; and fault tolerance, assessed by the network's ability to maintain operations during component failures. Redundancy mechanisms like the Spanning Tree Protocol (STP), standardized in IEEE 802.1D, prevent loops in bridged networks by dynamically blocking redundant paths while allowing failover, thus enhancing overall reliability. Internet-scale connectivity relies on inter-domain routing protocols to achieve global reachability. The Border Gateway Protocol (BGP), version 4 as defined in RFC 4271, enables routers in different autonomous systems—independent networks under single administrative control—to exchange routing information and select optimal paths based on policy attributes like path length and preferences. This policy-driven approach supports the internet's decentralized structure, where approximately 85,000 autonomous systems (as of November 2025) interconnect to form a resilient global fabric.^[29]^[30] Historically, connectivity evolved from the ARPANET, launched in 1969 by the U.S. Department of Defense's Advanced Research Projects Agency to link research computers via packet switching, serving as the precursor to the internet.^[31] As address exhaustion loomed with IPv4's 32-bit limit, the transition to IPv6, specified in RFC 2460, introduced 128-bit addressing to accommodate exponential growth in connected devices, ensuring scalable long-term connectivity.^[32]

Data and System Integration

Data and system integration refers to the processes and technologies that enable seamless communication and data exchange between disparate software systems, databases, and applications, fostering interoperability in computing environments. This connectivity layer abstracts underlying network protocols to focus on data formats, protocols, and middleware that ensure reliable, scalable interactions. In modern information technology, such integration is essential for building distributed systems that can handle complex workflows across organizational boundaries. Database connectivity standards like Open Database Connectivity (ODBC) and Java Database Connectivity (JDBC) provide standardized interfaces for applications to query and manipulate data in remote databases. ODBC, developed by Microsoft in 1992, allows client applications to access relational databases through a common API, supporting drivers for various database management systems such as SQL Server and Oracle. JDBC, introduced by Sun Microsystems in 1997, extends similar functionality specifically for Java applications, enabling SQL queries over networks with platform independence. To optimize performance in high-demand scenarios, connection pooling techniques are employed, where a pool of pre-established database connections is maintained and reused, reducing the overhead of repeated connection setups and improving throughput in multi-user environments. API connectivity facilitates direct system-to-system interactions through well-defined interfaces, with RESTful services emerging as a dominant architectural style for web-based integrations. Representational State Transfer (REST), formalized by Roy Fielding in his 2000 dissertation, uses HTTP methods for stateless operations on resources identified by URIs, enabling scalable and cacheable data exchanges. GraphQL, developed by Facebook in 2012 and open-sourced in 2015, offers a query language for APIs that allows clients to request precisely the data needed, reducing over-fetching compared to traditional REST endpoints and improving efficiency in mobile and frontend applications. Authentication in these APIs is commonly secured via OAuth 2.0, an authorization framework standardized by the IETF in 2012, which delegates access without sharing credentials, supporting token-based flows for third-party integrations. In enterprise settings, integration patterns mediated by Enterprise Service Bus (ESB) architectures decouple applications through centralized middleware that routes messages and transforms data formats. ESB systems, popularized in the early 2000s, employ patterns such as publish-subscribe for broadcasting events to multiple subscribers and message queuing for asynchronous communication, ensuring fault-tolerant data flows in heterogeneous environments. Apache Kafka, an open-source distributed event streaming platform released in 2011, exemplifies message queuing in ESB-like setups, handling high-throughput data pipelines with durability and partitioning for real-time processing in applications like log aggregation and stream analytics. Cloud connectivity extends these principles to distributed infrastructures, where hybrid models combine on-premises and cloud resources for unified operations. Virtual Private Cloud (VPC) peering, as implemented in AWS since 2014, allows private IP connectivity between VPCs in different accounts or regions without traversing the public internet, enabling secure data transfer in multi-cloud or hybrid setups. API gateways serve as entry points for managing cloud-based integrations, providing features like rate limiting, authentication, and request transformation to orchestrate traffic between microservices and external clients. Despite these advancements, challenges persist in connected systems, particularly latency in microservices architectures where distributed components introduce delays that can degrade performance in synchronous calls. Security concerns have also evolved, with zero-trust models—advocated by NIST in its 2020 publication—gaining prominence post-2020 to address breaches in perimeter-based systems by enforcing continuous verification of all connections, regardless of origin.

Biology

Neural Connectivity

Neural connectivity refers to the intricate network of synaptic and structural links between neurons that enable information processing in the brain. Synapses serve as the primary junctions for neuronal communication, divided into chemical and electrical types. Chemical synapses transmit signals via neurotransmitters released from presynaptic vesicles, binding to receptors on the postsynaptic membrane, while electrical synapses allow direct ion flow through gap junctions formed by connexin proteins. These connections exhibit plasticity, adapting to activity levels through mechanisms like long-term potentiation (LTP), which strengthens synapses via NMDA receptor activation and AMPA receptor insertion, and long-term depression (LTD), which weakens them through endocannabinoid signaling and receptor endocytosis.^[33]^[34]^[35] At a larger scale, brain networks form interconnected systems mapped as connectomes, revealing organizational principles such as small-world properties—characterized by high clustering and short path lengths—that optimize efficient information transfer with minimal wiring costs. Techniques like diffusion tensor imaging (DTI) reconstruct white matter tracts by tracking water diffusion anisotropy, while functional MRI (fMRI) measures blood-oxygen-level-dependent signals to infer synchronized activity, as in the default mode network (DMN), which activates during introspection and includes hubs in the posterior cingulate cortex and medial prefrontal cortex. Neural graphs, modeled using graph theory, quantify these networks' topology, with metrics like modularity highlighting segregated yet integrated modules.^[36]^[37]^[38] During development, axonal guidance cues orchestrate precise wiring. Netrins, secreted proteins acting as attractants via DCC/UNC-40 receptors, promote axon extension toward midline targets, whereas semaphorins, often repellents through plexin/neuropilin complexes, steer axons away from inhibitory zones, ensuring topographic mapping in regions like the visual system. Disruptions in these cues can lead to miswiring, contributing to neurodevelopmental disorders. In autism spectrum disorder (ASD), the under-connectivity hypothesis posits reduced long-range functional correlations, particularly in fronto-temporal networks, evidenced by lower rs-fMRI coherence between DMN and task-positive areas. Schizophrenia involves disrupted rs-fMRI correlations, with aberrant hyper- and hypo-connectivity in salience and executive networks, linking to symptoms like hallucinations.^[39]^[40]^[41]^[42] Advanced techniques probe these connections dynamically. Optogenetics uses light-sensitive opsins, like channelrhodopsin-2, to selectively activate or silence neuron populations, mapping causal influences in circuits such as fear conditioning pathways in the amygdala. Recent 2020s advances include high-throughput synaptic mapping in vivo via two-photon optogenetics, enabling connectivity inference at single-synapse resolution. In model organisms, whole-brain connectome reconstruction in C. elegans—with its 302 neurons and ~7,000 synapses—has progressed through serial electron microscopy, with 2021 updates refining gap junction annotations and 2024 integrations linking connectomes to activity recordings for functional predictions.^[43]^[44]^[45]^[46]

Ecological Connectivity

Ecological connectivity refers to the processes and structures that enable the movement of organisms, energy, and nutrients across landscapes, facilitating interactions among populations and ecosystems. In ecology, it encompasses the linkages between habitats that support species dispersal, gene flow, and trophic interactions, countering the isolating effects of habitat fragmentation caused by human activities such as urbanization and agriculture. Fragmentation reduces connectivity by creating isolated patches, leading to decreased biodiversity and increased extinction risks, as evidenced by studies showing that habitat loss disrupts metapopulation dynamics where subpopulations in separate patches rely on dispersal for persistence.^[47]^[48] Habitat connectivity is primarily maintained through ecological corridors—linear features like riparian zones or wildlife underpasses—that link fragmented patches, allowing species to move between them and form metapopulations. Metapopulations are groups of spatially separated populations that interact via dispersal, enhancing overall viability; for instance, increased connectivity has been shown to boost colonization rates and reduce local extinctions in dynamic habitats. The SLOSS debate highlights a key controversy in conservation planning: whether a single large reserve (SL) preserves more species than several small ones (SS), with evidence suggesting that connectivity between small patches can sometimes outperform isolated large ones by promoting gene flow and rescue effects, though outcomes depend on species mobility and landscape context. Fragmentation exacerbates these issues by increasing edge effects and isolation, potentially halving metapopulation persistence in patchy landscapes.^[49]^[50]^[51] Trophic connectivity describes the networked interactions in food webs, where species are linked through predator-prey and mutualistic relationships, influencing ecosystem stability. Food webs exhibit structural motifs such as chains and loops; mutualism chains, involving reciprocal benefits like pollination networks, enhance resilience by diversifying energy flows and buffering against perturbations. Network stability increases with trophic coherence—a measure of how well trophic levels align—reducing oscillation risks in dynamic systems, as demonstrated in analyses of real-world food webs. However, excessive connectivity can introduce instability if it amplifies cascading effects, underscoring the balance needed in trophic structures.^[52]^[53]^[54] Genetic connectivity arises from gene flow driven by organismal dispersal, maintaining genetic diversity across populations and countering inbreeding depression in fragmented habitats. Measured by F_ST statistics, which quantify differentiation between subpopulations (F_ST = 0 indicates panmixia, while higher values signal isolation), gene flow integrates multi-generational dispersal patterns to reveal effective connectivity. Low F_ST values in connected landscapes reflect higher dispersal success, as seen in studies of montane species where barriers reduce gene flow, leading to elevated differentiation. This connectivity is crucial for adaptive potential, particularly under environmental pressures.^[55]^[56]^[57] Conservation efforts prioritize restoring ecological connectivity to safeguard biodiversity, with wildlife corridors serving as targeted interventions. The Yellowstone to Yukon (Y2Y) initiative exemplifies this, spanning over 3,200 km to link protected areas and facilitate grizzly bear and other species movements, achieving over 50% expansion in protected lands and key corridors since the 2000s. Climate change amplifies the need for such measures, as shifting ranges due to warming necessitate broader connectivity to enable species migration; for example, corridors help species track suitable habitats amid projected range shifts of hundreds of kilometers by 2100. Post-2000s expansions in Y2Y have incorporated climate-resilient designs, integrating Indigenous knowledge and multi-stakeholder planning.^[58]^[59]^[60] Key metrics quantify landscape connectivity to guide conservation, with the Integral Index of Connectivity (IIC) being widely used for its focus on habitat availability and pairwise patch connections. IIC is calculated as the sum of connections between all habitat pairs, normalized by total habitat area squared, ranging from 0 (no connectivity) to 1 (full connectivity); it effectively captures fragmentation thresholds, dropping sharply as habitat loss approaches 50% or more (remaining habitat below 10-50%) in many systems, with thresholds varying by species and landscape. Applied in tools like Conefor software, IIC prioritizes corridor placements by identifying nodes that maximize overall connectivity gains.^[61]^[62]^[63]

Physics

Percolation Theory

Percolation theory models the emergence of long-range connectivity in disordered systems, particularly on lattices where sites or bonds are randomly occupied with probability p. Introduced by Broadbent and Hammersley in 1957, it distinguishes between site percolation, where vertices are occupied, and bond percolation, where edges are present. Below a critical occupation probability p_c, only finite clusters form; at p_c, an infinite cluster appears, marking a geometric phase transition. For site percolation on the two-dimensional square lattice, p_c \approx 0.5927.^[64] Near p_c, cluster properties follow scaling theory, where the probability of belonging to the infinite cluster, P_\infty, scales as P_\infty \sim (p - p_c)^\beta for p > p_c, with \beta the order parameter exponent, and the mean cluster size diverges as \chi \sim |p - p_c|^{-\gamma}, with \gamma the susceptibility exponent. Finite clusters dominate below p_c, while above it, the infinite cluster spans the system, enabling connectivity across the lattice. These exponents satisfy hyperscaling relations, providing a framework for understanding critical behavior in random media. In applications to conductivity of disordered materials, percolation describes how electrical transport emerges when conductive paths connect at p_c, with effective conductivity scaling as \sigma \sim (p - p_c)^t near the threshold, where t is a conductivity exponent. Renormalization group methods, developed by Wilson in the 1970s for critical phenomena, were adapted to percolation in the mid-1970s to compute fixed points and exponents analytically.^[65] Percolation exhibits universality classes, where critical exponents depend on dimensionality and lattice type but not microscopic details; for instance, two-dimensional systems have exact exponents like \beta = 5/36, differing from three-dimensional values around \beta \approx 0.41. Directed percolation extends the model to nonequilibrium dynamics with oriented bonds, defining a distinct universality class for absorbing-state transitions. Bootstrap percolation, developed in the 1990s, modifies the process with deterministic spreading: initially occupied sites infect neighbors once a threshold number of neighbors are occupied, leading to cellular automata-like cluster growth and sharp metastability thresholds.^[66]

Quantum Systems

In quantum physics, connectivity manifests through phenomena like entanglement, where distant particles exhibit correlations that defy classical notions of locality. The Einstein-Podolsky-Rosen (EPR) paradox, proposed in 1935, highlighted this by arguing that quantum mechanics implies instantaneous influences between separated systems, challenging the completeness of the theory and suggesting hidden variables to restore local realism.^[67] John Bell's 1964 theorem formalized this tension, deriving inequalities that any local hidden-variable theory must satisfy; violations by quantum predictions, such as those in Bell states—maximally entangled two-qubit states like the singlet |\Psi^-\rangle = \frac{1}{\sqrt{2}} (|01\rangle - |10\rangle)—demonstrate non-local correlations inherent to quantum connectivity.^[68] These states enable perfect anti-correlation in measurements, underscoring how quantum links transcend spatial separation without signal transmission. Quantum networks extend this connectivity over distances by distributing entanglement, countering losses from decoherence—the irreversible loss of quantum superpositions due to environmental interactions that suppress coherent superpositions.^[69] Measures like concurrence quantify the "connectedness" of entangled pairs, defined for a two-qubit density matrix \rho as C(\rho) = \max(0, \sqrt{\lambda_1} - \sqrt{\lambda_2} - \sqrt{\lambda_3} - \sqrt{\lambda_4}), where \lambda_i are eigenvalues of \rho (\sigma_y \otimes \sigma_y) \rho^* (\sigma_y \otimes \sigma_y), providing a scale from 0 (separable) to 1 (maximally entangled).^[70] The Duan-Lukin-Cirac-Zoller (DLCZ) protocol, introduced in 2001, uses atomic ensembles and linear optics to create quantum repeaters that generate and purify entanglement via heralded photon emissions, enabling scalable distribution over kilometers by nesting entanglement swapping and purification steps. Applications of quantum connectivity include the quantum internet, envisioned as a network for secure communication and distributed computing via shared entanglement. Proposals from the 2010s, building on earlier frameworks, outline architectures where nodes connect through quantum channels and classical links to perform tasks like teleportation and blind computing. In many-body systems, such as one-dimensional spin chains, connectivity arises from propagating entanglement, where interactions like the Heisenberg Hamiltonian H = J \sum_i \vec{S}_i \cdot \vec{S}_{i+1} generate area-law scaling of entanglement entropy near critical points, revealing phase transitions and quantum information flow.^[71] Experimental milestones include the 2015 loophole-free Bell test using entangled electron spins separated by 1.3 km, violating the CHSH inequality by over 2 standard deviations and confirming non-locality without detection or locality loopholes,^[72] and the 2017 Micius satellite demonstration, which distributed entangled photons over 1200 km, achieving a Bell violation parameter S = 2.37 \pm 0.09 and fidelity above 0.80 to a Bell state.^[73] More recent advancements as of 2025 include Purdue University's quantum network testbed, which demonstrated photonic entanglement distribution across multiple nodes in a metropolitan setting,^[74] and a scalable testbed in Berlin using metropolitan fibers to achieve robust high-fidelity entanglement distribution over large distances.^[75]

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Many task-based fMRI studies show that individuals with ASD exhibit reduced functional connectivity between multiple cortical regions or between cortical and ...
[40]
Abnormal Neural Connectivity in Schizophrenia and fMRI ... - Frontiers
Mar 21, 2013 · The present article summarizes the findings coming from hemodynamics-based neuroimaging that support the abnormal connectivity hypothesis in schizophrenia.
[41]
Light Up the Brain: The Application of Optogenetics in Cell-Type ...
In this review, we will first highlight the use of optogenetics in the investigation of neural connectivity, both within and between brain regions, and then ...
[42]
High-throughput synaptic connectivity mapping using in vivo two ...
Sep 17, 2025 · Here, we present an experimental and computational strategy for in vivo high-throughput synaptic connectivity mapping in which optogenetics and ...
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Wired For Insight- Recent Advance in C. elegans Neural Circuits
This mini-review aims to provide an overview of new information on connectomics and progress towards a molecular atlas of C. elegans nervous system.
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Bridging the gap between the connectome and whole-brain activity ...
Sep 23, 2024 · The nematode C. elegans is at the forefront of this question because its connectome is known, recordings of whole-brain neural activity at ...
[45]
Survival in patchy landscapes: the interplay between dispersal ...
Jul 7, 2015 · Habitat loss and fragmentation are important factors determining animal population dynamics and spatial distribution.Introduction · Results · DiscussionMissing: debate | Show results with:debate
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Ongoing accumulation of plant diversity through habitat connectivity ...
Sep 27, 2019 · Habitat connectivity has increased rates of colonization and decreased rates of extinction. As communities assembled, connectivity increased the ...
[47]
Metapopulation responses to patch connectivity and quality are ...
We found that patch occupancy did not significantly increase with increasing patch connectivity in dynamic habitat, whereas there was a strong positive ...
[48]
Resolving the SLOSS dilemma for biodiversity conservation - NIH
The legacy of the 'SL > SS principle', that a single or a few large habitat patches (SL) conserve more species than several small patches (SS), ...
[49]
The interplay between dispersal, habitat loss and fragmentation
Aug 6, 2025 · Habitat loss and fragmentation are important factors determining animal population dynamics and spatial distribution.
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Trophic coherence determines food-web stability | PNAS
Here we show that food webs (networks describing who eats whom in an ecosystem) exhibit a property we call trophic coherence, a measure of how neatly the ...Missing: motifs | Show results with:motifs
[51]
Network analysis suggests changes in food web stability produced ...
Jun 27, 2022 · The trophic relationships between predator and prey constitute the food web and it represents a network of the energy channels in an ecosystem.Missing: connectivity motifs
[52]
Motif analysis in directed ordered networks and applications to food ...
Jul 6, 2015 · We present a technique to calculate the fine grained motif spectrum by resolving the individual members of isomorphism classes.
[53]
Indirect measures of gene flow and migration: F ST ≠1/(4Nm+1)
Feb 1, 1999 · The difficulty of directly measuring gene flow has lead to the common use of indirect measures extrapolated from genetic frequency data.
[54]
Spatial coalescent connectivity through multi-generation dispersal ...
Oct 4, 2022 · Gene flow governs the contemporary spatial structure and dynamic of populations as well as their long-term evolution. For species that disperse ...
[55]
[PDF] Genetic diversity and gene flow decline with elevation in montane ...
May 10, 2017 · Our results provide insights into patterns of dispersal and connectivity in montane stream biota distributed over elevation gradients ...
[56]
Yellowstone to Yukon (Y2Y): Connecting and protecting one the of ...
Aug 8, 2022 · Protected areas increased more than 50% across the Y2Y region, and a number of ecological corridors and other areas conserving connectivity have ...
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Wildlife Corridors | U.S. Fish & Wildlife Service
Whether they run, swim or fly, wild animals need to move to complete their life cycles. We call their routes wildlife corridors. These can span anywhere ...
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Wildlife Corridors: Background and Issues for Congress
Jan 13, 2025 · Wildlife corridors are components of the landscape that are managed to create or improve ecological connectivity for one or more species.
[59]
Ecological networks: Pursuing the shortest path, however narrow ...
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Additive effects of connectivity provided by different habitat types ...
Sep 27, 2019 · How connectivity affects plant assemblages is a central issue in landscape ecology. So far, empirical studies have produced contradictory ...Introduction · Discussion · Methods
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fort / ecosystems-lcp_connectivity · GitLab - USGS.gov
Jul 26, 2022 · Integral index of connectivity (iic). Definition: Index developed specifically for landscapes based on habitat availability and a binary ...
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Site percolation threshold for square lattice - IOPscience
In order to find out as precisely as possible the site percolation threshold in the square lattice, a Fortran high speed Monte Carlo program has been developed ...
[63]
A renormalization group theory for percolation problems - IOPscience
A renormalization group approach to two-dimensional bond percolation problems is developed using a scaling transformation in real space.
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Critical points of two-dimensional bootstrap percolation-like cellular ...
Critical points of two-dimensional bootstrap percolation-like cellular automata. Short Communications; Published: March 1990. Volume 58, pages 1239–1244, (1990) ...
[65]
Can Quantum-Mechanical Description of Physical Reality Be ...
Einstein and his coauthors claimed to show that quantum mechanics led to logical contradictions. The objections exposed the theory's strangest ...
[66]
On the Einstein Podolsky Rosen paradox | Physics Physique Fizika
On the Einstein Podolsky Rosen paradox. JS Bell. Department of Physics, University of Wisconsin, Madison, Wisconsin.
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Decoherence, einselection, and the quantum origins of the classical
May 22, 2003 · Reprinted 1983 in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton University, Princeton, NJ), p. 87. Bohr, N.
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Entanglement of Formation of an Arbitrary State of Two Qubits
Mar 9, 1998 · The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.
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Ground state entanglement in quantum spin chains - arXiv
Mar 25, 2004 · The paper calculates ground state entanglement in XY and Heisenberg models, showing universal scaling at phase transitions, controlled by ...
[70]
Loophole-free Bell inequality violation using electron spins ... - Nature
Oct 21, 2015 · Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality.
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Satellite-based entanglement distribution over 1200 kilometers
Jun 16, 2017 · Here we demonstrate satellite-based distribution of entangled photon pairs to two locations separated by 1203 kilometers on Earth.