Pair Of Paths Research Articles

Effects on the algebraic connectivity of weighted graphs under edge rotations

For a weighted graph G, the rotation of an edge uv1 from v1 to a vertex v2 is defined as follows: delete the edge uv1, set w(uv2) as w(uv1)+w(uv2) if uv2 is an edge of G; otherwise, add a new edge uv2 and set w(uv2)=w(uv1), where w(uv1) and w(uv2) are the weights of the edges uv1 and uv2, respectively. In this paper, effects on the algebraic connectivity of weighted graphs under edge rotations are studied. For a weighted graph, a sufficient condition for an edge rotation to reduce its algebraic connectivity and a necessary condition for an edge rotation to improve its algebraic connectivity are proposed based on Fiedler vectors of the graph. As applications, we show that, by using a series of edge rotations, a pair of pendent paths (a pendent tree) of a weighted graph can be transformed into one pendent path (pendent edges attached at a common vertex) of the graph with the algebraic connectivity decreasing (increasing) monotonically. These results extend previous findings of reducing the algebraic connectivity of unweighted graphs by using edge rotations.

A Maslov-Type Index in Dimension 2

In this article, we define an index of the Maslov type for paths of 2×2 orthogonal symplectic matrices. The starting point is an arbitrary 2×2 orthogonal symplectic matrix rather than the identity matrix. We use this index to explain the geometric intersection number of a pair of Lagrangian paths and compare it with the Cappell–Lee–Miller index.

Enhanced FRER Mechanism in Time-Sensitive Networking for Reliable Edge Computing.

Time-Sensitive Networking (TSN) and edge computing are promising networking technologies for the future of the Industrial Internet. TSN provides a reliable and deterministic low-latency communication service for edge computing. The Frame Replication and Elimination for Reliability (FRER) mechanism is important for improving the network reliability of TSN. It achieves high reliability by transmitting identical frames in parallel on two disjoint paths, while eliminating duplicated frames at the destination node. However, there are two problems with the FRER mechanism. One problem is that it does not consider the path reliability, and the other one is that it is difficult to find two completely disjoint path pairs in some cases. To solve the above problems, this paper proposes a method to find edge-disjoint path pairs considering path reliability for FRER in TSN. The method includes two parts: one is building a reliability model for paths, and the other one is computing a working path and a redundant path with the Edge-Disjoint Path Pairs Selection (EDPPS) algorithm. Theoretical and simulation results show that the proposed method effectively improves path reliability while reducing the delay jitter of frames. Compared with the traditional FRER mechanism, the proposed method reduces delay jitter by 15.6% when the network load is 0.9.

The Feynman chessboard model in 3 + 1 dimensions

The chessboard model was Feynman’s adaptation of his path integral method to a two-dimensional relativistic domain. It is shown that chessboard paths encode information about the contiguous pairs of paths in a spacetime plane, as required by discrete worldlines in Minkowski space. The application of coding by pairs in a four-dimensional spacetime is then restricted by the requirements of the Lorentz transformation, and the implementation of these restrictions provides an extension of the model to 4D, illuminating the relationship between relativity and quantum propagation.

Comparison Analysis of Graph Theory Algorithms for Shortest Path Problem

The Sumba region, Indonesia, is known for its extraordinary natural beauty and unique cultural richness. There are 19 interesting tourist attractions spread throughout the area, but tourists often face difficulties in planning efficient visiting routes. From this case, it can be solved by applying graph theory in terms of searching for the shortest distance which is completed using the shortest path search algorithm. Then these 19 tourist objects are used to build a weighted graph, where the nodes represent the tourist objects and the edges of the graph describe the distance or travel time between these objects. Therefore, this research aims to compare the shortest path search algorithm with parameters to compare the shortest distance results, algorithm complexity and execution time for tourism in the Sumba area. The results of this research involve a comparison of several shortest path search algorithms, with the aim of finding the shortest distance results, algorithm complexity, and execution time for tourism in the Sumba area. Based on the test results of the five algorithms with the parameters that have been prepared, and the findings show that each algorithm has its own characteristics, the results are as follows: Dijkstra's algorithm can be used to calculate the shortest route for single-source and single-destination types. This resembles the Bellman-Ford algorithm, only the Bellman-Ford algorithm can be used simultaneously on graphs that have negative weight values. Meanwhile, the Floyd-Warshall algorithm is suitable for use on the all-pairs type. Then, the Johnson Algorithm can be used to determine the shortest path from all pairs of paths where the destination node is located in the graph. Finally, the Ant Colony algorithm to compute from a node to each pair of destination nodes.

A 1.5 mm2 4-Channel EEG/BIOZ Acquisition ASIC With 15.2-Bit 3-Step ADC Based on a Signal-Dependent Low-Power Strategy.

This article presents a multichannel EEG/BIOZ acquisition application specific integrated circuit (ASIC) with 4 EEG channels and a BIOZ channel, a switch resistor low-pass filter (SR-LPF). Each EEG channel includes a frontend, and a 4-channel multiplexed analog-to-digital converter (ADC), while the BIOZ channel features a pseudo sine current generator and a pair of readout paths with multiplexed SR-LPF and ADC. The ASIC is designed for size and power minimization, utilizing a 3-step ADC with a novel signal-dependent low power strategy. The proposed ADC operates at a sampling rate of 1600 S/s with a resolution of 15.2 bits, occupying only 0.093 mm2. With the help of the proposed signal-dependent low-power strategy, the ADC's power dissipation drops from 32.2 μW to 26.4 μW, resulting in an 18% efficiency improvement without performance degradation. Moreover, the EEG channels deliver excellent noise performance with a NEF of 7.56 and 27.8 nV/√Hz at the expense of 0.16 mm2 per channel. In BIOZ measurement, a 5-bit programmable current source is used to generate pseudo sine injection current ranging from 0 to 22 μApp, and the detection sensitivity reaches 2.4 mΩ/√Hz. Finally, the presented multichannel EEG/BIOZ acquisition ASIC has a compact active area of 1.5 mm2 in an 180nm CMOS technology.

CBDC-PUF: A Novel Physical Unclonable Function Design Framework Utilizing Configurable Butterfly Delay Chain Against Modeling Attack

Physical unclonable function (PUF) is a promising security-based primitive, which provides an extremely large number of responses for key generation and authentication applications. Various PUFs have been developed as central building blocks in cryptographic protocols and security architectures, however, the existing PUFs and their improvements are still vulnerable to modeling attacks (MA) with refined machine learning algorithms. In this article, a configurable butterfly delay chain-based PUF design framework is proposed to meet the requirements of randomness, reliability, uniqueness, and MA-resistance metrics. A configurable butterfly delay chain is introduced to create multiple pairs of symmetric paths and a strong PUF relying on the intrinsic delay fluctuations of two identical paths is built. Furthermore, a secure hash function is used to insert non-linearities into the PUF, and a BCH-based error correction algorithm is utilized to recover the actual responses under noisy environments. The proposed PUF is implemented on Xilinx FPGAs and three machine learning algorithms are used to evaluate the resistance against MA. Experimental results show that the randomness, reliability, and uniqueness of the proposed PUF are close to the ideal value (49.6%, 99.9%, and 49.9%, respectively), and the prediction accuracy reaches 50% that indicating a desirable resilient to MA.

Physically non-cloneable arbiter -type function with non-linear path pairs

Physically unclonable functions (PUFs) are basic physical cryptographical primitives, providing to solve tasks such as unclonable identification, digital device authentication and copyright authentication, true random sequence generation, etc. The major features of PUFs are stability, unpredictability and irreproducibility, due to uncontrollable random variations of distinctive features of the raw materials and technological processes used during their manufacturing. Generally, PUF are digital circuits that extract such variations and convert them into a binary format, which applied for further use. Among the variety of PUF types, an Arbiter PUF (APUF) is distinguished, which is a digital circuit with N-bit challenge input and single output for one-bit response generation. The functionality of APUF is based on comparison of transition time of two copies of the test signal along a pair of configurable paths, selected by the challenge value CH from a set of 2N all possible pairs. The result of the comparison is the binary value of the response. The set of all challenge-response pairs is a random, unpredictable and irreproducible in the cases of implementation of cloned PUF circuits both on single and/or on another chips, also using different technologies. This article presents a new approach to the synthesis of the APUF circuits, based on the permutation network elements, which allow to construct the nonlinear structures of pair of paths. This implies the potential complication of building an APUF model to attack its implemented instances. This article presents new schematic solutions for the synthesis of APUF circuits. Also, the main characteristics of the proposed APUF circuits implemented on the Xilinx Zynq-7000 FPGA is analyzed.

Automatic Balancing of “Arbiter” Physical Unclonable Function Paths

The features of building on the basis of programmable logic integrated circuits of “arbiter” physical unclonable functions (APUF) are considered. The problem of asymmetry of pairs of APUF paths is indicated and the negative impact of this phenomenon on their characteristics is noted. A time measuring system based on a ring oscillator scheme, which is used to analyze the time characteristics of APUF paths, is described. A method for automatic balancing of signal propagation delays through the APUF paths based on the calculation of the corrective value is proposed. The consistency of the proposed balancing technique is experimentally confirmed based on the improvement in the characteristics of the APUF after its implementation. A digital scheme of this technique is presented, which can form the basis for the development of a delay auto correction scheme through APUF paths with different levels of autonomy.

An exact approach for finding bicriteria maximally SRLG-disjoint/shortest path pairs in telecommunication networks

The paper addresses a bicriteria optimisation problem in telecommunication networks that aims at finding Pareto efficient pairs of paths between two given nodes, seeking to minimise the number of SRLGs (Shared Risk Link Groups) common to both paths and the path pair cost. This problem is of particular importance in telecommunication routing design, namely concerning resilient routing models where both a primary and a backup paths have to be calculated to minimise the risk of failure of a connection between origin and terminal nodes, in case of failure in the primary path. An exact resolution method is applied for solving this problem, enabling the calculation of the whole set of Pareto optimal solutions, which combines a transformation of the network representation with a path ranking algorithm. A comprehensive experimental study on the application of this approach, using reference network topologies, considering random SRLG assignments to the links and random link bandwidth occupations, together with the discussion on typical examples of solution selection and potential advantages of the method, are presented.

On refinements of wilf-equivalence for involutions

Let $${\mathcal {S}}_n(\pi )$$ (resp. $${\mathcal {I}}_n(\pi )$$ and $$\mathcal{A}\mathcal{I}_n(\pi )$$ ) denote the set of permutations (resp. involutions and alternating involutions) of length n which avoid the permutation pattern $$\pi $$ . For $$k,m\ge 1$$ , Backelin–West–Xin proved that $$|{\mathcal {S}}_n(12\cdots k\tau )|= |{\mathcal {S}}_n(k\cdots 21\tau )|$$ by establishing a bijection between these two sets, where $$\tau = \tau _1\tau _2\cdots \tau _m$$ is an arbitrary permutation of $$k+1,k+2,\ldots ,k+m$$ . The result has been extended to involutions by Bousquet-Mélou and Steingrímsson and to alternating permutations by the first author. In this paper, we shall establish a peak set preserving bijection between $${\mathcal {I}}_n(123\tau )$$ and $${\mathcal {I}}_n(321\tau )$$ via transversals, matchings, oscillating tableaux and pairs of noncrossing Dyck paths as intermediate structures. Our result is a refinement of the result of Bousquet-Mélou and Steingrímsson for the case when $$k=3$$ . As an application, we show bijectively that $$|\mathcal{A}\mathcal{I}_n(123\tau )| = |\mathcal{A}\mathcal{I}_n(321\tau )|$$ , confirming a recent conjecture of Barnabei–Bonetti–Castronuovo–Silimbani. Furthermore, some conjectured equalities posed by Barnabei–Bonetti–Castronuovo–Silimbani concerning pattern-avoiding alternating involutions are also proved.

2D physically unclonable functions of the arbiter type

Objectives. The problem of constructing a new class of physically unclonable functions of the arbiter type (APUF) is being solved, based on the difference in delay times for the inputs of numerous modifications of the base element, due to both an increase in the number of inputs and the topology of their connection. Such an approach allows building two-dimensional physically unclonable functions (2D-APUF), in which, unlike classical APUF, the challenge generated for each basic element selects a pair of paths not from two possible, but from a larger number of them. The relevance of such a study is associated with the active development of physical cryptography. The following goals are pursued in the work: the construction of the basic elements of the APUF and their modifications, the development of a methodology for constructing 2D-APUF.Methods. The methods of synthesis and analysis of digital devices are used, including those based on programmable logic integrated circuits, the basics of Boolean algebra and circuitry. Results. It is shown that the classical APUF uses a standard basic element that performs two functions, namely, the function of choosing a pair of paths Select and the function of switching paths Switch, which, due to their joint use, allow achieving high performance. First of all, this concerns the stability of the APUF functioning, which is characterized by a small number of challenge, for which the response randomly takes one of two possible values 0 or 1. Modifications of the base element in terms of the implementations of its Select and Switch functions are proposed. New structures of the base element are presented in which the modifications of their implementations are made, including in terms of increasing the number of pairs of paths of the base element from which one of them is selected by the challenge, and the configurations of their switching. The use of various basic elements makes it possible to improve the main characteristics of APUF, as well as to break the regularity of their structure, which was the main reason for hacking APUF through machine learning. Conclusion. The proposed approach to the construction of physically unclonable 2D-APUF functions, based on the difference in signal delays through the base element, has shown its efficiency and promise. The effect of improving the characteristics of such PUFs has been experimentally confirmed with noticeable improvement in the stability of their functioning. It seems promising to further develop the ideas of constructing two-dimensional physically unclonable functions of the arbiter type, as well as experimental study of their characteristics, as well as resistance to various types of attacks, including using machine learning.

Interaction between Everett Worlds and Fundamental Decoherence in Non-Unitary Newtonian Gravity

It is shown that the non-unitary Newtonian gravity (NNG) model admits a simple interpretation in terms of the Feynman path integral, in which the sum over all possible histories is replaced by a summation over pairs of paths. Correlations between different paths are allowed by a fundamental decoherence mechanism of gravitational origin and can be interpreted as a kind of communication between different branches of the wave function. The ensuing formulation could be used in turn as a motivation to introduce non-unitary gravity itself.

A Time Impulse Neural Network Framework for Solving the Minimum Path Pair Problems of the Time-Varying Network

The minimum path pair (MPP) query problem is to find the optimal meeting point of two minimum paths for two users in a network, where each user's minimum path has its own departure and destination nodes. However, the MPP query problem on a time-varying network that generally exists in the world remains open. In this study, we investigate the time-varying minimum path pair (TMPP) query problem, where the arcs of the network are time dependent. We first model the TMPP and then propose a time impulse neural network (TINN) to solve the TMPP. In the design of the TINN, the entire network topology is considered as the architecture of the neural network, and each node is viewed as a neuron. The core of an impulse-based neuron consists of six parts: input, impulse receiver, time window selector, neuron storage, impulse sender, and output. Unlike the traditional neural network, the whole neural network does not require a training process but is implemented through an impulse mechanism. The TINN consists of two stages; the first stage is to find the two minimum paths of two users, while the second stage is to calculate the distance between these two minimum paths. The underlying idea of the TINN is to find the minimum path using an impulse mechanism. The minimum path relies on the earliest time impulse stemming from the depart node that arrives at the destination node. With this mechanism, both the minimum path of the network and the distance between two paths can be addressed. Furthermore, theoretical analysis demonstrates the correctness and provides the complexity of the TINN. Experiments of the TINN are carried out based on the well-known New York City Map. A comparative study illustrates the effectiveness of the TINN.

An efficient and effective method for reliability assessment of project duration

ABSTRACT The reliability assessment of the project duration is essential for successful project management; this has prompted the development of various methods to assess whether a project will be completed within the target duration. In this study, an efficient and effective method for assessing the reliability of project duration based on the method of moments is proposed, which utilizes bivariate-dimension reduction technology and the third-moment reliability index. The proposed method can avoid the extensive calculations of various factors in the commonly used methods: the correlation coefficients between each pair of paths and the joint failure probability of each pair of representative paths. From two numerical examples, it can be concluded that the proposed method can obtain almost the same results as Monte Carlo simulations with less calculation.

Continuum models of directed polymers on disordered diamond fractals in the critical case

We construct and study a family of random continuum polymer measures Mr corresponding to limiting partition function laws recently derived in a weak-coupling regime for polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval [0,1] into a compact diamond fractal having Hausdorff dimension two, and there is a natural “uniform” probability measure, μ, over the space of directed paths, Γ. Realizations of the random path measures Mr exhibit strong localization properties in comparison to their subcritical counterparts in which the diamond fractal has dimension less than two. Whereas two paths p,q∈Γ sampled independently using the pure measure μ have only finitely many intersections with probability one, a realization of the disordered product measure Mr×Mr a.s. assigns positive weight to the set of pairs of paths (p,q) whose intersection sets are uncountable but of Hausdorff dimension zero. We give a more refined characterization of the size of these dimension-zero sets using generalized (logarithmic) Hausdorff measures. The law of the random measure Mr cannot be constructed as a subcritical Gaussian multiplicative chaos because the coupling strength to the Gaussian field would, in a formal sense, have to be infinite.

Finite Domination Type for Monoid Presentations

In [5], Squier, Otto and Kobayashi explored a homotopical property for monoids called finite derivation type (FDT) and proved that FDT is a necessary condition that a finitely presented monoid must satisfy if it is to have a finite canonical presentation. In the latter development in [2], Kobayashi proved that the property <img src=image/13428295_01.gif> is equivalent with what is called in [2] finite domination type. It was indicated in the end of [2] that there are <img src=image/13428295_01.gif> monoids which are not even finitely generated, and as a consequence are not of FDT. It was this indication that inspired us to look for the possibility of defining a property of monoids which encapsulates both, FDT and finite domination type. This is realized in the current paper by extending the notion of finite domination from monoids to rewriting systems, and to achieve this, we are based on the approach of Isbell in [1], who defined the notion of the dominion of a subcategory <img src=image/13428295_02.gif> of a category <img src=image/13428295_03.gif> and characterized that dominion in terms of zigzags in <img src=image/13428295_03.gif> over <img src=image/13428295_02.gif>. The reason we followed this approach is that to every rewriting system <img src=image/13428295_04.gif> which gives a monoid <img src=image/13428295_06.gif>, there is always a category <img src=image/13428295_05.gif> associated to it which contains three types of information at the same time: (i) all the possible ways in which the elements of <img src=image/13428295_06.gif> are written in terms of words with letters from <img src=image/13428295_07.gif>, (ii) all the possible ways one can transform a word with letters from <img src=image/13428295_07.gif> into another one representing the same element of <img src=image/13428295_06.gif> by using rewriting rules from <img src=image/13428295_08.gif>. Each of such way gives is in fact a path in the reduction graph of <img src=image/13428295_04.gif>. The last information (iii) encoded in <img src=image/13428295_05.gif> is that <img src=image/13428295_05.gif> contains all the possible ways that two parallel paths of the reduction graph are linked to each other by a series of compositions of whiskerings of other parallel paths. This category <img src=image/13428295_05.gif> turns out to have the advantage that it can "measure" the extent to which a set <img src=image/13428295_09.gif> of parallel paths is sufficient to express any pair of parallel paths by composing whiskers from <img src=image/13428295_09.gif>. The gadget used to measure this, is the Isbell dominion of the whisker category <img src=image/13428295_10.gif> generated by <img src=image/13428295_09.gif> over <img src=image/13428295_05.gif>. We then define the monoid <img src=image/13428295_06.gif> given by <img src=image/13428295_04.gif> to be of finite domination type (FDOT) if both <img src=image/13428295_07.gif> and <img src=image/13428295_08.gif> are finite and there is a finite set <img src=image/13428295_09.gif> of morphisms such that <img src=image/13428295_11.gif> is exactly <img src=image/13428295_05.gif>. The first main result of our paper is that likewise FDT, FDOT is an invariant of the monoid presentation, and the second one is that that FDT implies FDOT, while remains open whether the converse is true or not. The importance of FDOT stands in the fact that not only it generalizes FDT, but the way it is defined has a lot in common with <img src=image/13428295_01.gif>, giving thus hope that FDOT is the right tool to put FDT and <img src=image/13428295_01.gif> into the same framework.

Protons in Gating the Kv1.2 Channel: A Calculated Set of Protonation States in Response to Polarization/Depolarization of the Channel, with the Complete Proposed Proton Path from Voltage Sensing Domain to Gate.

We have in the past proposed that proton motion constitutes the gating current in the potassium channel Kv1.2 and is responsible for the gating mechanism. For this to happen, there must be a proton path between the voltage-sensing domain (VSD) and the channel gate, and here we present quantum calculations that lead to a specific pair of proton paths, defined at the molecular level, with well-defined water molecule linkages, and with hydrogen bonding between residues; there is also at least one interpath crossover, where protons can switch paths. Quantum calculations on the entire 563-atom system give the complete geometry, the energy, and atomic charges. Calculations show that three specific residues (in the pdb 3Lut numbering, H418, E327, R326), and the T1 intracellular moiety, all of which have been shown experimentally to be involved in gating, would necessarily be protonated or deprotonated in the path between the VSD and the gate. Hydroxyl reorientation of serine and threonine residues are shown to provide a means of adjusting proton directions of motion. In the deprotonated state for K312, a low energy state, our calculations come close to reproducing the X-ray structure. The demonstration of the existence of a double proton path between VSD and gate supports the proposed proton gating mechanism; when combined with our earlier demonstration of proton generation in the VSD, and comparison with other systems that are known to move protons, we are close to achieving the definition of a complete gating mechanism in molecular detail. The coupling of the paths to the VSD, and to the PVPV section that essentially forms the gate, can be easily seen from the results of the calculation. The gate itself remains for further computations.

Arbiter Physical Unclonable Functions with Asymmetric Pairs of Paths

The methods of constructing physical unclonable functions (PUF), which are the basis of physical cryptography, are analyzed. The broad applicability of the Arbiter PUF, based on the analysis of the delays of the signal transmitted along two paths, is noted. It is shown that the randomness of the delays is explained by technological variations in the manufacturing process of PUF and their dependence on the use of homogeneous repeating elements that ensure the symmetry of the paths. As an alternative to the existing solutions, the article proposes a new approach for constructing an Arbiter PUF based on asymmetric paths. The sources of randomness as logical element delays are investigated. Their diversity and distinctive characteristics are shown depending on the number of inputs to which an active signal is supplied and the values at other inputs. A technique for balancing a set of pairs of paths of Arbiter PUF is proposed, which lays in regulating the duration of the impulse test signal depending on four types of path asymmetry. New structures of Arbiter PUF with asymmetric pairs of paths are proposed. Experimental studies confirm the possibility of using various sources of randomness in the form of signal delays.

Counting lattice paths by crossings and major index I: the corner-flipping bijections

We solve two problems regarding the enumeration of lattice paths in \(\mathbb{Z}^2\) with steps \((1,1)\) and \((1,-1)\) with respect to the major index, defined as the sum of the positions of the valleys, and to the number of certain crossings. The first problem considers crossings of a single path with a fixed horizontal line. The second one counts pairs of paths with respect to the number of times they cross each other. Our proofs introduce lattice path bijections with convenient visual descriptions, and the answers are given by remarkably simple formulas involving \(q\)-binomial coefficients.Mathematics Subject Classifications: 05A19, 05A15, 05A30Keywords: Lattice path, major index, crossing, valley, bijection