Optimizing Thermochromism of Solution-Processed VO2_2 Nanocomposite Films for Chromogenic Fenestration

Vanadium (IV) oxide is one of the most promising materials for thermochromic films due to its unique, reversible crystal phase transition from monoclinic (M1) to rutile (R) at its critical temperature (T$_c$) which corresponds to a change in optical properties: above T$_c$, VO$_2$ films exhibit a decreased transmittance for wavelengths of light in the near-infrared region. However, a high transmittance modulation often sacrifices luminous transmittance which is necessary for commercial and residential applications of this technology. In this study, we explore the potential for synthesis of VO$_2$ films in a matrix of metal oxide nanocrystals, using In$_2$O$_3$, TiO$_2$, and ZnO as diluents. We seek to optimize the annealing conditions to yield desirable optical properties. Although the films diluted with TiO$_2$ and ZnO failed to show transmittance modulation, those diluted with In$_2$O$_3$ exhibited strong thermochromism. Our investigation introduces a novel window film consisting of a 0.93 metal ionic molar ratio VO$_2$-In$_2$O$_3$ nanocrystalline matrix, demonstrating a significant increase in luminous transmittance without any measurable impact on thermochromic character. Furthermore, solution-processing mitigates costs, allowing this film to be synthesized 4x-7x cheaper than industry standards. This study represents a crucial development in film chemistry and paves the way for further application of VO$_2$ nanocomposite films in chromogenic fenestration.Comment: 14 pages, 18 figure

Spectral Implications of Variability in GRB Fireballs

Cosmological $\gamma$-ray bursts originate from relativistic winds. Temporal fluctuations in the wind velocity can give rise to internal shocks which dissipate a significant fraction of the wind kinetic energy. Part of the energy dissipated is transferred to the electrons through Fermi acceleration. If the post shock fluid is strongly magnetized, the relativistic electrons cool initially through synchrotron emission, and later through Compton scattering. The upsacttered radiation triggers a cascade of $e^{+}e^{-}$-pairs. We compute the final spectrum for a wide range of parameter values for the emission region. We show that the spectral diversity observed by BATSE can be naturally explained by emission from internal shocks, which are associated with the observed source variability.Comment: 3 pages, 1 figure; talk given at the VIII Marcel Grossmann Meeting on General Relativity, Jerusalem, June 1997 (to appear in the proceedings

Average value of solutions of the bipartite quadratic assignment problem and linkages to domination analysis

In this paper we study the complexity and domination analysis in the context of the \emph{bipartite quadratic assignment problem}. Two variants of the problem, denoted by BQAP1 and BQAP2, are investigated. A formula for calculating the average objective function value $\mathcal{A}$ of all solutions is presented whereas computing the median objective function value is shown to be NP-hard. We show that any heuristic algorithm that produces a solution with objective function value at most $\mathcal{A}$ has the domination ratio at least $\frac{1}{mn}$. Analogous results for the standard \emph{quadratic assignment problem} is an open question. We show that computing a solution whose objective function value is no worse than that of $n^mm^n-{\lceil\frac{n}{\alpha}\rceil}^{\lceil\frac{m}{\alpha}\rceil}{\lceil\frac{m}{\alpha}\rceil}^{\lceil\frac{n}{\alpha}\rceil}$ solutions of BQAP1 or $m^mn^n-{\lceil\frac{m}{\alpha}\rceil}^{\lceil\frac{m}{\alpha}\rceil}{\lceil\frac{n}{\alpha}\rceil}^{\lceil\frac{n}{\alpha}\rceil}$ solutions of BQAP2, is NP-hard for any fixed natural numbers $a$ and $b$ such that $\alpha=\frac{a}{b}>1$. However, a solution with the domination number $\Omega(m^{n-1}n^{m-1}+m^{n+1}n+mn^{m+1})$ for BQAP1 and $\Omega(m^{m-1}n^{n-1}+m^2n^{n}+m^mn^2)$ for BQAP2, can be found in $O(m^3n^3)$ time

Fair Outlier Detection

An outlier detection method may be considered fair over specified sensitive attributes if the results of outlier detection are not skewed towards particular groups defined on such sensitive attributes. In this task, we consider, for the first time to our best knowledge, the task of fair outlier detection. In this work, we consider the task of fair outlier detection over multiple multi-valued sensitive attributes (e.g., gender, race, religion, nationality, marital status etc.). We propose a fair outlier detection method, FairLOF, that is inspired by the popular LOF formulation for neighborhood-based outlier detection. We outline ways in which unfairness could be induced within LOF and develop three heuristic principles to enhance fairness, which form the basis of the FairLOF method. Being a novel task, we develop an evaluation framework for fair outlier detection, and use that to benchmark FairLOF on quality and fairness of results. Through an extensive empirical evaluation over real-world datasets, we illustrate that FairLOF is able to achieve significant improvements in fairness at sometimes marginal degradations on result quality as measured against the fairness-agnostic LOF method.Comment: In Proceedings of The 21th International Conference on Web Information Systems Engineering (WISE 2020), Amsterdam and Leiden, The Netherland

A characterization of linearizable instances of the quadratic minimum spanning tree problem

We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph $G=(V,E)$ that can be solved as a linear minimum spanning tree problem. Characterization of such problems on graphs with special properties are given. This include complete graphs, complete bipartite graphs, cactuses among others. Our characterization can be verified in $O(|E|^2)$ time. In the case of complete graphs and when the cost matrix is given in factored form, we show that our characterization can be verified in $O(|E|)$ time. Related open problems are also indicated

The generalized vertex cover problem and some variations

In this paper we study the generalized vertex cover problem (GVC), which is a generalization of various well studied combinatorial optimization problems. GVC is shown to be equivalent to the unconstrained binary quadratic programming problem and also equivalent to some other variations of the general GVC. Some solvable cases are identified and approximation algorithms are suggested for special cases. We also study GVC on bipartite graphs and identify some polynomially solvable cases. We show that GVC on bipartite graphs is equivalent to the bipartite unconstrained 0-1 quadratic programming problem. Integer programming formulations of GVC and related problems are presented and establish half-integrality property on some variables for the corresponding linear programming relaxations. We also discuss special cases of GVC where all feasible solutions are independent sets or vertex covers. These problems are observed to be equivalent to the maximum weight independent set problem or minimum weight vertex cover problem along with some algorithmic results.Comment: 24 page

Heuristic algorithms for the bipartite unconstrained 0-1 quadratic programming problem

We study the Bipartite Unconstrained 0-1 Quadratic Programming Problem (BQP) which is a relaxation of the Unconstrained 0-1 Quadratic Programming Problem (QP). Applications of the BQP include mining discrete patterns from binary data, approximating matrices by rank-one binary matrices, computing cut-norm of a matrix, and solving optimization problems such as maximum weight biclique, bipartite maximum weight cut, maximum weight induced subgraph of a bipartite graph, etc. We propose several classes of heuristic approaches to solve the BQP and discuss a number of construction algorithms, local search algorithms and their combinations. Results of extensive computational experiments are reported to establish the practical performance of our algorithms. For this purpose, we propose several sets of test instances based on various applications of the BQP. Our algorithms are compared with state-of-the-art heuristics for QP which can also be used to solve BQP with reformulation. We also study theoretical properties of the neighborhoods and algorithms. In particular, we establish complexity of all neighborhood search algorithms and establish tight worst-case performance ratio for the greedy algorithm.Comment: 17 page

Bottleneck flows in networks

The bottleneck network flow problem (BNFP) is a generalization of several well-studied bottleneck problems such as the bottleneck transportation problem (BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and so on. In this paper we provide a review of important results on this topic and its various special cases. We observe that the BNFP can be solved as a sequence of $O(\log n)$ maximum flow problems. However, special augmenting path based algorithms for the maximum flow problem can be modified to obtain algorithms for the BNFP with the property that these variations and the corresponding maximum flow algorithms have identical worst case time complexity. On unit capacity network we show that BNFP can be solved in $O(\min \{{m(n\log n)}^{{2/3}}, m^{{3/2}}\sqrt{\log n}\})$. This improves the best available algorithm by a factor of $\sqrt{\log n}$. On unit capacity simple graphs, we show that BNFP can be solved in $O(m \sqrt {n \log n})$ time. As a consequence we have an $O(m \sqrt {n \log n})$ algorithm for the BTP with unit arc capacities

Representations of quadratic combinatorial optimization problems: A case study using the quadratic set covering problem

The objective function of a quadratic combinatorial optimization problem (QCOP) can be represented by two data points, a quadratic cost matrix Q and a linear cost vector c. Different, but equivalent, representations of the pair (Q, c) for the same QCOP are well known in literature. Research papers often state that without loss of generality we assume Q is symmetric, or upper-triangular or positive semidefinite, etc. These representations however have inherently different properties. Popular general purpose 0-1 QCOP solvers such as GUROBI and CPLEX do not suggest a preferred representation of Q and c. Our experimental analysis discloses that GUROBI prefers the upper triangular representation of the matrix Q while CPLEX prefers the symmetric representation in a statistically significant manner. Equivalent representations, although preserve optimality, they could alter the corresponding lower bound values obtained by various lower bounding schemes. For the natural lower bound of a QCOP, symmetric representation produced tighter bounds, in general. Effect of equivalent representations when CPLEX and GUROBI run in a heuristic mode are also explored. Further, we review various equivalent representations of a QCOP from the literature that have theoretical basis to be viewed as strong and provide new theoretical insights for generating such equivalent representations making use of constant value property and diagonalization (linearization) of QCOP instances.Comment: 36 page

New Results on the Existence of Open Loop Nash Equilibria in Discrete Time Dynamic Games

We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). The classical approach to DTDGs involves analyzing the problem using optimal control theory which yields results mainly limited to linear-quadratic games. We show the existence of equilibria for a class of DTDGs where the cost function of players admits a quasi-potential function which leads to new results and, in some cases, a generalization of similar results from linear-quadratic games. Our results are obtained by introducing a new formulation for analysing DTDGs using the concept of a conjectured state by the players. In this formulation, the state of the game is modelled as dependent on players. Using this formulation we show that there is an optimisation problem such that the solution of this problem gives an equilibrium of the DTDG. To extend the result for more general games, we modify the DTDG with an additional constraint of consistency of the conjectured state. Any equilibrium of the original game is also an equilibrium of this modified game with consistent conjectures. In the modified game, we show the existence of equilibria for DTDGs where the cost function of players admits a potential function. We end with conditions under which an equilibrium of the game with consistent conjectures is an $\epsilon$-Nash equilibria of the original game.Comment: 12 pages, under review with the IEEE Transactions on Automatic Contro