Congestion Control for Network-Aware Telehaptic Communication

Telehaptic applications involve delay-sensitive multimedia communication between remote locations with distinct Quality of Service (QoS) requirements for different media components. These QoS constraints pose a variety of challenges, especially when the communication occurs over a shared network, with unknown and time-varying cross-traffic. In this work, we propose a transport layer congestion control protocol for telehaptic applications operating over shared networks, termed as dynamic packetization module (DPM). DPM is a lossless, network-aware protocol which tunes the telehaptic packetization rate based on the level of congestion in the network. To monitor the network congestion, we devise a novel network feedback module, which communicates the end-to-end delays encountered by the telehaptic packets to the respective transmitters with negligible overhead. Via extensive simulations, we show that DPM meets the QoS requirements of telehaptic applications over a wide range of network cross-traffic conditions. We also report qualitative results of a real-time telepottery experiment with several human subjects, which reveal that DPM preserves the quality of telehaptic activity even under heavily congested network scenarios. Finally, we compare the performance of DPM with several previously proposed telehaptic communication protocols and demonstrate that DPM outperforms these protocols.Comment: 25 pages, 19 figure

Optimal transmission switching and grid reconfiguration for transmission systems via convex relaxations

In this paper, we formulate optimization problems to perform optimal transmission switching (OTS) in order to operate power transmission grids most efficiently. In any given electrical network, several of the transmission lines are generally equipped with switches, circuit breakers, and/or reclosers. The conventional practice is to operate the grid using a static or fixed configuration. However, it may be beneficial to dynamically reconfigure the grid through switching actions in order to respond to real-time demand and supply conditions. This has the potential to help reduce costs and improve efficiency. Furthermore, such OTS may be more crucial in future power grids with much higher penetrations of renewable energy sources, which introduce more variability and intermittency in generation. Similarly, OTS can potentially help mitigate the effects of unpredictable demand fluctuations (e.g. due to extreme weather). We explored and compared several different formulations for the OTS problems in terms of computational performance and optimality. I also applied them to small transmission test case networks as a proof of concept to see what the effects of applying OTS are

Local retail electricity markets for distribution grid services

We propose a hierarchical local electricity market (LEM) at the primary and secondary feeder levels in a distribution grid, to optimally coordinate and schedule distributed energy resources (DER) and provide valuable grid services like voltage control. At the primary level, we use a current injection-based model that is valid for both radial and meshed, balanced and unbalanced, multi-phase systems. The primary and secondary markets leverage the flexibility offered by DERs to optimize grid operation and maximize social welfare. Numerical simulations on an IEEE-123 bus modified to include DERs, show that the LEM successfully achieves voltage control and reduces overall network costs, while also allowing us to decompose the price and value associated with different grid services so as to accurately compensate DERs.Comment: 9 pages, 13 figures, submitted to 7th IEEE Conference on Control Technology and Applications (CCTA) 202

A Defeasible Logic of Policy-based Intention

Most of the theories on formalising intention interpret it as a unary modal operator in Kripkean semantics, which gives it a monotonic look. We argue that policy-based intentions exhibit non-monotonic behaviour which could be captured through a non-monotonic system like defeasible logic. The proposed technique alleviates most of the problems related to logical omniscience

Separation Between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth Three Circuits

We show an exponential separation between two well-studied models of algebraic computation, namely read-once oblivious algebraic branching programs (ROABPs) and multilinear depth three circuits. In particular we show the following: 1. There exists an explicit n-variate polynomial computable by linear sized multilinear depth three circuits (with only two product gates) such that every ROABP computing it requires 2^{Omega(n)} size. 2. Any multilinear depth three circuit computing IMM_{n,d} (the iterated matrix multiplication polynomial formed by multiplying d, n * n symbolic matrices) has n^{Omega(d)} size. IMM_{n,d} can be easily computed by a poly(n,d) sized ROABP. 3. Further, the proof of 2 yields an exponential separation between multilinear depth four and multilinear depth three circuits: There is an explicit n-variate, degree d polynomial computable by a poly(n,d) sized multilinear depth four circuit such that any multilinear depth three circuit computing it has size n^{Omega(d)}. This improves upon the quasi-polynomial separation result by Raz and Yehudayoff [2009] between these two models. The hard polynomial in 1 is constructed using a novel application of expander graphs in conjunction with the evaluation dimension measure used previously in Nisan [1991], Raz [2006,2009], Raz and Yehudayoff [2009], and Forbes and Shpilka [2013], while 2 is proved via a new adaptation of the dimension of the partial derivatives measure used by Nisan and Wigderson [1997]. Our lower bounds hold over any field

Reconstruction of Full Rank Algebraic Branching Programs

An algebraic branching program (ABP) A can be modelled as a product expression X_1 X_2 ... X_d, where X_1 and X_d are 1 x w and w x 1 matrices respectively, and every other X_k is a w x w matrix; the entries of these matrices are linear forms in m variables over a field F (which we assume to be either Q or a field of characteristic poly(m)). The polynomial computed by A is the entry of the 1 x 1 matrix obtained from the product X_1 X_2 ... X_d. We say A is a full rank ABP if the w^2(d-2) + 2w linear forms occurring in the matrices X_1, X_2, ...X_d are F-linearly independent. Our main result is a randomized reconstruction algorithm for full rank ABPs: Given blackbox access to an m-variate polynomial f of degree at most m, the algorithm outputs a full rank ABP computing f if such an ABP exists, or outputs \u27no full rank ABP exists\u27 (with high probability). The running time of the algorithm is polynomial in m and b, where b is the bit length of the coefficients of f. The algorithm works even if X_k is a w_{k-1} x w_k matrix (with w_0 = w_d = 1), and v = (w_1, ..., w_{d-1}) is unknown. The result is obtained by designing a randomized polynomial time equivalence test for the family of iterated matrix multiplication polynomial IMM_{v,d}, the (1,1)-th entry of a product of d rectangular symbolic matrices whose dimensions are according to v in N^{d-1}. At its core, the algorithm exploits a connection between the irreducible invariant subspaces of the Lie algebra of the group of symmetries of a polynomial f that is equivalent to IMM_{v,d} and the \u27layer spaces\u27 of a full rank ABP computing f. This connection also helps determine the group of symmetries of IMM_{v,d} and show that IMM_{v,d} is characterized by its group of symmetries

Randomized Polynomial-Time Equivalence Between Determinant and Trace-IMM Equivalence Tests

Equivalence testing for a polynomial family {g_m} over a field F is the following problem: Given black-box access to an n-variate polynomial f(x), where n is the number of variables in g_m, check if there exists an A in GL(n,F) such that f(x) = g_m(Ax). If yes, then output such an A. The complexity of equivalence testing has been studied for a number of important polynomial families, including the determinant (Det) and the two popular variants of the iterated matrix multiplication polynomial: IMM_{w,d} (the (1,1) entry of the product of d many w $\times$ w symbolic matrices) and Tr-IMM_{w,d} (the trace of the product of d many w $\times$ w symbolic matrices). The families Det, IMM and Tr-IMM are VBP-complete, and so, in this sense, they have the same complexity. But, do they have the same equivalence testing complexity? We show that the answer is 'yes' for Det and Tr-IMM (modulo the use of randomness). The result is obtained by connecting the two problems via another well-studied problem called the full matrix algebra isomorphism problem (FMAI). In particular, we prove the following: 1. Testing equivalence of polynomials to Tr-IMM_{w,d}, for d$\geq$ 3 and w$\geq$ 2, is randomized polynomial-time Turing reducible to testing equivalence of polynomials to Det_w, the determinant of the w $\times$ w matrix of formal variables. (Here, d need not be a constant.) 2. FMAI is randomized polynomial-time Turing reducible to equivalence testing (in fact, to tensor isomorphism testing) for the family of matrix multiplication tensors {Tr-IMM_{w,3}}. These in conjunction with the randomized poly-time reduction from determinant equivalence testing to FMAI [Garg,Gupta,Kayal,Saha19], imply that FMAI, equivalence testing for Tr-IMM and for Det, and the $3$-tensor isomorphism problem for the family of matrix multiplication tensors are randomized poly-time equivalent under Turing reductions.Comment: 36 pages, 2 figure