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

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

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

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

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

Upper Limit on the Milky Way Mass from the Orbit of the Sagittarius Dwarf Satellite

As one of the most massive Milky Way satellites, the Sagittarius dwarf galaxy has played an important role in shaping the Galactic disk and stellar halo morphologies. The disruption of Sagittarius over several close-in passages has populated the halo of our Galaxy with large-scale tidal streams and offers a unique diagnostic tool for measuring its gravitational potential. Here we test different progenitor mass models for the Milky Way and Sagittarius by modeling the full infall of the satellite. We constrain the mass of the Galaxy based on the observed orbital parameters and multiple tidal streams of Sagittarius. Our semi-analytic modeling of the orbital dynamics agrees with full $N$-body simulations, and favors low values for the Milky Way mass, $\lesssim 10^{12}M_\odot$. This conclusion eases the tension between $\Lambda$CDM and the observed parameters of the Milky Way satellites.Comment: Accepted by ApJ; 11 page

Stochastic reachability of a target tube: Theory and computation

Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within time-varying state constraints (i.e., a ``target tube''), despite bounded control authority. This problem subsumes the stochastic viability and terminal hitting-time stochastic reach-avoid problems. Of special interest is the stochastic reach set, the set of all initial states from which it is possible to stay in the target tube with a probability above a desired threshold. We provide sufficient conditions under which the stochastic reach set is closed, compact, and convex, and provide an underapproximative interpolation technique for stochastic reach sets. Utilizing convex optimization, we propose a scalable and grid-free algorithm that computes a polytopic underapproximation of the stochastic reach set and synthesizes an open-loop controller. This algorithm is anytime, i.e., it produces a valid output even on early termination. We demonstrate the efficacy and scalability of our approach on several numerical examples, and show that our algorithm outperforms existing software tools for verification of linear systems

Combinatorial Optimization Problems with Interaction Costs: Complexity and Solvable Cases

We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear costs and the interaction costs between elements of the two selected structures is minimized. COPIC generalizes the quadratic assignment problem and many other well studied combinatorial optimization problems, and hence covers many real world applications. We show how various topics from different areas in the literature can be formulated as special cases of COPIC. The main contributions of this paper are results on the computational complexity and approximability of COPIC for different families of combinatorial structures (e.g. spanning trees, paths, matroids), and special structures of the interaction costs. More specifically, we analyze the complexity if the interaction cost matrix is parameterized by its rank and if it is a diagonal matrix. Also, we determine the structure of the intersection cost matrix, such that COPIC is equivalent to independently solving linear optimization problems for the two given families of combinatorial structures

The Quadratic Minimum Spanning Tree Problem and its Variations

The quadratic minimum spanning tree problem and its variations such as the quadratic bottleneck spanning tree problem, the minimum spanning tree problem with conflict pair constraints, and the bottleneck spanning tree problem with conflict pair constraints are useful in modeling various real life applications. All these problems are known to be NP-hard. In this paper, we investigate these problems to obtain additional insights into the structure of the problems and to identify possible demarcation between easy and hard special cases. New polynomially solvable cases have been identified, as well as NP-hard instances on very simple graphs. As a byproduct, we have a recursive formula for counting the number of spanning trees on a $(k,n)$-accordion and a characterization of matroids in the context of a quadratic objective function