Search

Combined electric power system and High-Altitude Electromagnetic Pulse (HEMP) models are being developed to determine the effect of a HEMP on the US power grid. The work relies primarily on deterministic methods; however, it is computationally untenable to evaluate the E1 HEMP response of large numbers of grid components distributed across a large interconnection. Further, the deterministic assessment of these components' failures are largely unachievable. E1 HEMP laboratory testing of the components is accomplished, but is expensive, leaving few data points to construct failure models of grid components exposed to E1 HEMP. The use of Bayesian priors, developed using the subject matter expertise, combined with the minimal test data in a Bayesian inference process, provides the basis for the development of more robust and cost-effective statistical component failure models. These can be used with minimal computational burden in a simulation environment such as sampling of Cumulative Distribution Functions (CDFs).

Amidst the COVID-19 pandemic, with many organizations, schools, colleges, and universities transitioning to virtual platforms, students encountered difficulties in acquiring PCs such as desktops or laptops. The starting prices, around 15,000 INR, often failed to offer adequate system specifications, posing a challenge for consumers. Additionally, those reliant on laptops for work found the conventional approach cumbersome. Enter the "Portable Smart Computer," a leap into the future of computing. This innovative device boasts speed and performance comparable to traditional desktops but in a compact, energy-efficient, and cost-effective package. It delivers a seamless desktop experience, whether one is editing documents, browsing multiple tabs, managing spreadsheets, or creating presentations. Moreover, it supports programming languages like Python, C, C++, as well as compilers such as Keil and Xilinx, catering to the needs of programmers., Comment: 34 pages

The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint distribution of all unknown variables implied by the statistical model that will be used to analyze the collected data. The utility function defines the objective of the experiment where a common utility function is the information gain. This article introduces an expanded framework for this process, where we go beyond the traditional Expected Information Gain criteria and introduce the Expected General Information Gain which measures robustness to the model discrepancy and Expected Discriminatory Information as a criterion to quantify how well an experiment can detect model discrepancy. The functionality of the framework is showcased through its application to a scenario involving a linearized spring mass damper system and an F-16 model where the model discrepancy is taken into account while doing Bayesian optimal experiment design.

In this paper, we study shared cache coded caching (SC-CC): a set of caches serves a larger set of users; each user access one cache, and a cache may serve many users. For this problem, under uncoded placement, Parrinello, \"Unsal, and Elia showed an optimal SC-CC scheme, in which the subpacketization level depends upon the number of caches. We show an SC-CC scheme where the subpacketization level does not directly depend upon the number of users or caches; any number of caches and users can be accommodated for a fixed subpacketization level. Furthermore, new caches can be added without re-doing the placement of the existing caches. We show that given an upper limit on the allowable subpacketization level, our SC-CC scheme may achieve a lesser rate than other relevant SC-CC schemes. Our scheme is constructed using matrices and designs. A matroid can be obtained from a matrix over a finite field; the placement of our scheme is decided by a design constructed from a matrix; the circuits of a matroid obtained from the matrix and the design is used to decide the delivery., Comment: 36 pages, the paper has been submitted to IEEE Transactions on Information Theory

In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and Hinf-norm based correction for a linear Gaussian system. As the dimension of state or parameter space grows, performing the full Kalman update with the dense covariance matrix for a large scale system requires increased storage and computational complexity, making it impractical. The VIF approach, based on mean-field Gaussian variational inference, reduces this burden through the variational approximation to the covariance usually in the form of a diagonal covariance approximation. The challenge is to retain convergence and correct for biases introduced by the sequential VIF steps. We desire a framework that improves feasibility while still maintaining reasonable proximity to the optimal Kalman filter as data is assimilated. To accomplish this goal, a Hinf-norm based optimization perturbs the VIF covariance matrix to improve robustness. This yields a novel VIF- Hinf recursion that employs consecutive variational inference and Hinf based optimization steps. We explore the development of this method and investigate a numerical example to illustrate the effectiveness of the proposed filter.

Balancing model complexity against the information contained in observed data is the central challenge to learning. In order for complexity-efficient models to exist and be discoverable in high dimensions, we require a computational framework that relates a credible notion of complexity to simple parameter representations. Further, this framework must allow excess complexity to be gradually removed via gradient-based optimization. Our n-ary, or n-argument, activation functions fill this gap by approximating belief functions (probabilistic Boolean logic) using logit representations of probability. Just as Boolean logic determines the truth of a consequent claim from relationships among a set of antecedent propositions, probabilistic formulations generalize predictions when antecedents, truth tables, and consequents all retain uncertainty. Our activation functions demonstrate the ability to learn arbitrary logic, such as the binary exclusive disjunction (p xor q) and ternary conditioned disjunction ( c ? p : q ), in a single layer using an activation function of matching or greater arity. Further, we represent belief tables using a basis that directly associates the number of nonzero parameters to the effective arity of the belief function, thus capturing a concrete relationship between logical complexity and efficient parameter representations. This opens optimization approaches to reduce logical complexity by inducing parameter sparsity.

We study the problem of multi-access coded caching (MACC): a central server has $N$ files, $K$ ($K \leq N$) caches each of which stores $M$ out of the $N$ files, $K$ users each of which demands one out of the $N$ files, and each user accesses $z$ caches. The objective is to jointly design the placement, delivery, and user-to-cache association, to optimize the achievable rate. This problem has been extensively studied in the literature under the assumption that a user accesses only one cache. However, when a user accesses more caches, this problem has been studied only under the assumption that a user accesses $z$ consecutive caches with a cyclic wrap-around over the boundaries. A natural question is how other user-to-cache associations fare against the cyclic wrap-around user-to-cache association. A bipartite graph can describe a general user-to-cache association. We identify a class of bipartite graphs that, when used as a user-to-cache association, achieves either a lesser rate or a lesser subpacketization than all other existing MACC schemes using a cyclic wrap-around user-to-cache association. The placement and delivery strategy of our MACC scheme is constructed using a combinatorial structure called maximal cross resolvable design., Comment: 34 pages, 5 figures and 3 tables

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the l1 norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to a) determine redundant sensing architectures for linear time invariant systems, b) accurately estimate states with low-cost sensors, and c) optimally schedule sensors for linear time-varying systems., Comment: 26 pages, 6 figures

This paper addresses modeling and control of a six-degree-of-freedom unmanned aerial vehicle capable of vertical take-off and landing in the presence of wind disturbances. We design a hybrid vehicle that combines the benefits of both the fixed-wing and the rotary-wing UAVs. A non-linear model for the hybrid vehicle is rapidly built, combining rigid body dynamics, aerodynamics of wing, and dynamics of the motor and propeller. Further, we design an H2 optimal controller to make the UAV robust to wind disturbances. We compare its results against that of PID and LQR-based control. Our proposed controller results in better performance in terms of root mean squared errors and time responses during two scenarios: hover and level-flight., Comment: 7 pages, 13 figures

Tracking objects in Computer Vision is a hard problem. Privacy and utility concerns adds an extra layer of complexity over this problem. In this work we consider the problem of maintaining privacy and utility while tracking an object in a video stream using Kalman filtering. Our first proposed method ensures that the localization accuracy of this object will not improve beyond a certain level. Our second method ensures that the localization accuracy of the same object will always remain under a certain threshold., Comment: 6 pages, 5 figures

In this paper we are concerned with the error-covariance lower-bounding problem in Kalman filtering: a sensor releases a set of measurements to the data fusion/estimation center, which has a perfect knowledge of the dynamic model, to allow it to estimate the states, while preventing it to estimate the states beyond a given accuracy. We propose a measurement noise manipulation scheme to ensure lower-bound on the estimation accuracy of states. Our proposed method ensures lower-bound on the steady state estimation error of Kalman filter, using mathematical tools from eigen value analysis., Comment: 6 pages, 1 figure

In this work we propose a framework to address the issue of state dependent nonlinear equality-constrained state estimation using Bayesian filtering. This framework is constructed specifically for a linear approximation of Bayesian filtering that uses the theory of Optimal Transport. As a part of this framework, we present three traditionally-used nonlinear equality constraint-preserving algorithms coupled with the Optimal Transport based filter: the equality-constrained Optimal Transport filter, the projected Optimal Transport filter, and the measurement-augmented Optimal Transport filter. In cases where the nonlinear equality-constraints represent an arbitrary convex manifold, we show that the re-sampling step of Optimal Transport filter, can generate initial samples for filtering, from any probability distribution function defined on this manifold. We show numerical results using our proposed framework., Comment: 6 pages, 5 figures

We consider the problem of selecting an optimal set of sensor precisions to estimate the states of a non-linear dynamical system using an Ensemble Kalman filter and an Unscented Kalman filter, which uses random and deterministic ensembles respectively. Specifically, the goal is to choose at run-time, a sparse set of sensor precisions for active-sensing that satisfies certain constraints on the estimated state covariance. In this paper, we show that this sensor precision selection problem is a semidefinite programming problem when we use l1 norm over precision vector as the surrogate measure to induce sparsity. We formulate a sensor selection scheme over multiple time steps, for certain constraints on the terminal estimated state covariance., Comment: 8 pages, 4 figures

In this paper, we present an optimization-based formulation for privacy-utility tradeoff in the Ensemble and Unscented Kalman filtering framework, with a focus on space situational awareness. Privacy and utility are defined in terms of a lower and an upper bound on the state estimation error covariance, respectively. Synthetic sensor noise is used to satisfy these bounds and is determined by solving an optimization problem. Given privacy and utility bounds, we present optimization problem formulations to determine a) the maximum noise for which utility is satisfied or the estimation errors are upper-bounded, b) the minimum noise for which privacy is satisfied or the estimation errors are lower-bounded, c) the optimal noise that satisfies utility constraints and maximizes privacy, and d) the optimal noise that satisfies privacy constraints and maximizes utility. We demonstrate application of these formulations to the tracking of the International Space Station, and highlight the optimal privacy vs utility tradeoff for this dynamical system.

Consider the problem of registering multiple point sets in some $d$-dimensional space using rotations and translations. Assume that there are sets with common points, and moreover the pairwise correspondences are known for such sets. We consider a least-squares formulation of this problem, where the variables are the transforms associated with the point sets. The present novelty is that we reduce this nonconvex problem to an optimization over the positive semidefinite cone, where the objective is linear but the constraints are nevertheless nonconvex. We propose to solve this using variable splitting and the alternating directions method of multipliers (ADMM). Due to the linearity of the objective and the structure of constraints, the ADMM subproblems are given by projections with closed-form solutions. In particular, for $m$ point sets, the dominant cost per iteration is the partial eigendecomposition of an $md \times md$ matrix, and $m-1$ singular value decompositions of $d \times d$ matrices. We empirically show that for appropriate parameter settings, the proposed solver has a large convergence basin and is stable under perturbations. As applications, we use our method for $2$D shape matching and $3$D multiview registration. In either application, we model the shapes/scans as point sets and determine the pairwise correspondences using ICP. In particular, our algorithm compares favorably with existing methods for multiview reconstruction in terms of timing and accuracy., Comment: To appear in Computer Vision and Image Understanding (Elsevier)

It is known a vector linear solution may exist if and only if the characteristic of the finite field belongs to a certain set of primes. But, can increasing the message dimension make a network vector linearly solvable over a larger set of characteristics? To the best of our knowledge, there exists no network in the literature which has a vector linear solution for some message dimension if and only if the characteristic of the finite field belongs to a set $P$, and for some other message dimension it has a vector linear solution over some finite field whose characteristic does not belong to $P$. We have found that by \textit{increasing} the message dimension just by $1$, the set of characteristics over which a vector linear solution exists may get arbitrarily larger. However, somewhat surprisingly, we have also found that by \textit{decreasing} the message dimension just by $1$, the set of characteristics over which a vector linear solution exists may get arbitrarily larger. As a consequence of these finding, we prove two more results: (i) rings may be superior to finite fields in terms of achieving a scalar linear solution over a lesser sized alphabet, (ii) existences of $m_1$ and $m_2$ dimensional vector linear solutions guarantees the existence of an $(m_1 + m_2)$-dimensional vector linear solution only if the $m_1$ and $m_2$ dimensional vector linear solutions exist over the same finite field., Comment: Submitted to IEEE Transactions on Information Theory

It is known that for any finite/co-finite set of primes there exists a network which has a rate $1$ solution if and only if the characteristic of the finite field belongs to the given set. We generalize this result to show that for any positive rational number $k/n$, and for any given finite/co-finite set of primes, there exists a network which has a rate $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given set. For this purpose we construct two networks: $\mathcal{N}_1$ and $\mathcal{N}_2$; the network $\mathcal{N}_1$ has a $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given finite set of primes, and the network $\mathcal{N}_2$ has a $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given co-finite set of primes. Recently, a method has been introduced where characteristic-dependent linear rank inequalities are produced from networks whose linear coding capacity depends on the characteristic of the finite field. By employing this method on the networks $\mathcal{N}_1$ and $\mathcal{N}_2$, we construct two classes of characteristic-dependent linear rank inequalities. For any given set of primes, the first class contains an inequality which holds if the characteristic of the finite field does not belong to the given set of primes but may not hold otherwise; the second class contains an inequality which holds if the characteristic of the finite field belongs to the given set of primes but may not hold otherwise. We then use these inequalities to obtain an upper-bound on the linear coding capacity of $\mathcal{N}_1$ and $\mathcal{N}_2$., Comment: arXiv admin note: text overlap with arXiv:1610.08004

Sum-networks are networks where all the terminals demand the sum of the symbols generated at the sources. It has been shown that for any finite set/co-finite set of prime numbers, there exists a sum-network which has a vector linear solution if and only if the characteristic of the finite field belongs to the given set. It has also been shown that for any positive rational number $k/n$, there exists a sum-network which has capacity equal to $k/n$. It is a natural question whether, for any positive rational number $k/n$, and for any finite set/co-finite set of primes $\{p_1,p_2,\ldots,p_l\}$, there exists a sum-network which has a capacity achieving rate $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given set. We show that indeed there exists such a sum-network by constructing such a sum-network.

It is known that there exists a multiple-unicast network which has a rate $1$ linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co-finite set of primes. In this paper, we show that for any non-zero positive rational number $\frac{k}{n}$, there exists a multiple-unicast network which has a rate $\frac{k}{n}$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co-finite set of primes.

It is known that the Fano network has a vector linear solution if and only if the characteristic of the finite field is $2$; and the non-Fano network has a vector linear solution if and only if the characteristic of the finite field is not $2$. Using these properties of Fano and non-Fano networks it has been shown that linear network coding is insufficient. In this paper we generalize the properties of Fano and non-Fano networks. Specifically, by adding more nodes and edges to the Fano network, we construct a network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field belongs to an arbitrary given set of primes $\{p_1,p_2,\ldots,p_l\}$. Similarly, by adding more nodes and edges to the non-Fano network, we construct a network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field does not belong to an arbitrary given set of primes $\{p_1,p_2,\ldots,p_l\}$.

It is known that there exists a network, called as the M-network, which is not scalar linearly solvable but has a vector linear solution for message dimension two. Recently, a generalization of this result has been presented where it has been shown that for any integer $m\geq 2$, there exists a network which has a $(m,m)$ vector linear solution, but does not have a $(w,w)$ vector linear solution for $w