In this work, flame spread experiments with the flow applied in the opposite to the direction of spreading flame are conducted using 80 mm long cast PMMA cylinders of 1 mm diameter in the earth’s gravity and microgravity environments. The experiments are conducted at 23

In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive ratio O(log n log m) for the (general) online hitting set and set cover problems for m sets and n elements; this is known to be tight for efficient online algorithms. Given this barrier for general set systems, we ask: can we break this double-logarithmic phenomenon for online hitting set/set cover on structured and geometric set systems? We provide an O(log n loglog n)-competitive algorithm for the weighted online hitting set problem on set systems with linear shallow-cell complexity, replacing the double-logarithmic factor in the general result by effectively a single logarithmic term. As a consequence of our results we obtain the first bounds for weighted online hitting set for natural geometric set families, thereby answering open questions regarding the gap between general and geometric weighted online hitting set problems.

Sensitivity oracles preprocess a graph so that queries can be answered after any f edge insertions and deletions, without recomputing from scratch. For structural optimization problems the known landscape is limited: for flows and cuts, all known compact oracles handle only f≤2 failures; existing oracles for s- and global min-cut apply only to undirected graphs; and for matchings, arborescence and spanning-tree packings, and arboricity, no efficient oracle is known for f>1. We present a unified algebraic framework based on sensitivity oracles for matroid packing, covering, and parity of sparse linear matroids, yielding the first oracles supporting an arbitrary number f of updates across all of these problems (all constructions randomized Monte-Carlo). Concretely, we obtain efficient oracles for exact (s,t)-max-flow/min-cut, resolving an open problem of Baswana, Bhanja, and Pandey (ICALP'22) with near-optimal space; for all-pairs k-bounded flow, generalizing the near-optimal reachability oracle of Brand and Saranurak (FOCS'19, the case k=1); the first oracles for any f for directed s- and global min-cut; oracles for k-disjoint arborescences, k-disjoint spanning trees, colorful spanning trees, and arboricity; and oracles for the existence of an α-factor, with perfect matching as the case α=1. We further introduce the subset sensitivity model, in which updates are confined to a susceptible edge set of size σ fixed during preprocessing. Here we decouple updates from the matroid representation and eliminate the dependence on k and the matroid density altogether: all of the above are supported with O(f^ω) query time and O(fσ^2) space. We also prove a matching Ω(min{σ^2,n^2})-bit lower bound when f≥2, establishing optimality.

We consider the capacitated clustering problem in general metric spaces where the goal is to identify $k$ clusters and minimize the sum of the radii of the clusters (we call this the Capacitated-$k$-sumRadii problem). We are interested in fixed-parameter tractable (FPT) approximation algorithms where the running time is of the form $f(k) \cdot \text{poly}(n)$, where $f(k)$ can be an exponential function of $k$ and $n$ is the number of points in the input. In the uniform capacity case, Bandyapadhyay et al. recently gave a $4$-approximation algorithm for this problem. Our first result improves this to an FPT $3$-approximation and extends to a constant factor approximation for any $L_p$ norm of the cluster radii. In the general capacities version, Bandyapadhyay et al. gave an FPT $15$-approximation algorithm. We extend their framework to give an FPT $(4 + \sqrt{13})$-approximation algorithm for this problem. Our framework relies on a novel idea of identifying approximations to optimal clusters by carefully pruning points from an initial candidate set of points. This is in contrast to prior results that rely on guessing suitable points and building balls of appropriate radii around them. On the hardness front, we show that assuming the Exponential Time Hypothesis, there is a constant $c > 1$ such that any $c$-approximation algorithm for the non-uniform capacity version of this problem requires running time $2^{\Omega \left(\frac{k}{polylog(k)} \right)}$.

This study unveils an innovative approach to fabricating H2S gas sensor prototypes for continuous monitoring, leveraging Pd-decorated CuCrO2-based metal oxide semiconductor (MOS) chemiresistors and artificial neural network-assisted impedance-based multivariate analysis. Sensors were exposed to H2S in cross-interfering environments containing humidity, NO2, NH3, CH4, H2, and CO2. Impedance-based parameters (Z, phase difference, Z' and Z") obtained at various frequencies demonstrated that sensors were reproducible and selective for H2S detection. A neural network-based multilayer perceptron (MLP) regression model was trained with different impedance-based parameters to estimate the H2S concentrations. Continuous operation resulted in larger baseline variation for Z, Z', and Z" readings; however, the measured phase difference values exhibited less depletion than other parameters. Furthermore, concerns about baseline changes were effectively addressed with a fine-tuned MLP model, which predicted both pure air and H2S atmospheres more correctly under cross-interfering and baseline-depleted conditions by employing phase differences at different frequencies as input. Possible reasons for the accurate prediction can be attributed to the confined behaviour of phase difference and discussed with the help of sensor statistical parameters such as mean variation, standard deviation and principal components.

The field of learning-augmented algorithms seeks to use ML techniques on past instances of a problem to inform an algorithm designed for a future instance. In this paper, we introduce a novel model for learning-augmented algorithms inspired by online learning. In this model, we are given a sequence of instances of a problem and the goal of the learning-augmented algorithm is to use prior instances to propose a solution to a future instance of the problem. The performance of the algorithm is measured by its average performance across all the instances, where the performance on a single instance is the ratio between the cost of the algorithm's solution and that of an optimal solution for that instance. We apply this framework to the classic k-median clustering problem, and give an efficient learning algorithm that can approximately match the average performance of the best fixed k-median solution in hindsight across all the instances. We also experimentally evaluate our algorithm and show that its empirical performance is close to optimal, and also that it automatically adapts the solution to a dynamically changing sequence.

We study a two-institution stable matching model in which candidates from two distinct groups are evaluated using partially correlated signals that are group-biased. This extends prior work (which assumes institutions evaluate candidates in an identical manner) to a more realistic setting in which institutions rely on overlapping, but independently processed, criteria. These evaluations could consist of a variety of informative tools such as standardized tests, shared recommendation systems, or AI-based assessments with local noise. Two key parameters govern evaluations: the bias parameter $\beta \in (0,1]$, which models systematic disadvantage faced by one group, and the correlation parameter $\gamma \in [0,1]$, which captures the alignment between institutional rankings. We study the representation ratio $\mathcal{R}(\beta, \gamma)$, i.e., the ratio of disadvantaged to advantaged candidates selected by the matching process in this setting. Focusing on a regime in which all candidates prefer the same institution, we characterize the large-market equilibrium and derive a closed-form expression for the resulting representation ratio. Prior work shows that when $\gamma = 1$, this ratio scales linearly with $\beta$. In contrast, we show that $\mathcal{R}(\beta, \gamma)$ increases nonlinearly with $\gamma$ and even modest losses in correlation can cause sharp drops in the representation ratio. Our analysis identifies critical $\gamma$-thresholds where institutional selection behavior undergoes discrete transitions, and reveals structural conditions under which evaluator alignment or bias mitigation are most effective. Finally, we show how this framework and results enable interventions for fairness-aware design in decentralized selection systems.

Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparisonbased sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However, many real-world sorting applications operate in scenarios where the outcome of each comparison can be noisy. In this work, we explore settings where a bounded number of comparisons are potentially corrupted by erroneous agents, resulting in arbitrary, adversarial outcomes. We model the sorting problem as a query-limited tournament graph where edges involving erroneous nodes may yield arbitrary results. Our primary contribution is a randomized algorithm inspired by quick-sort that, in expectation, produces an ordering close to the true total order while only querying O (n) edges. We achieve a distance from the target order pi within (3+epsilon)|B|, where B is the set of erroneous nodes, balancing the competing objectives of minimizing both query complexity and misalignment with pi. Our algorithm needs to carefully balance two aspects - identify a pivot that partitions the vertex set evenly and ensure that this partition is "truthful" and yet query as few "triangles" in the graph G as possible. Since the nodes in B can potentially hide in an intricate manner, our algorithm requires several technical steps that ensure that progress is made in each recursive step. Additionally, we demonstrate significant implications for the Ulam-k-Median problem. This is a classical clustering problem where the metric is defined on the set of permutations on a set of d elements. Chakraborty, Das, and Krauthgamer gave a (2- epsilon) FPT approximation algorithm for this problem, where the running time is super-linear in both n and d. We give the first (2- epsilon) FPT linear time approximation algorithm for this problem. Our main technical result gives a strengthening of the results in Chakraborty et al. by showing that a good 1-median solution can be obtained from a constant-size random sample of the input. We use our robust sorting framework to find a good solution from such a random sample. We feel that the notion of robust sorting should have applications in several such settings.

Dementia is a neurological syndrome marked by cognitive decline. Alzheimer’s disease (AD) and frontotemporal dementia (FTD) are the common forms of dementia, each with distinct progression patterns. Early and accurate diagnosis of dementia cases (AD and FTD) is crucial for effective medical care, as both conditions have similar early-symptoms. EEG, a non-invasive tool for recording brain activity, has shown potential in distinguishing AD from FTD and mild cognitive impairment (MCI). This study aims to develop a deep learning-based classification system for dementia by analyzing EEG derived scout time-series signals from deep brain regions, specifically the hippocampus, amygdala, and thalamus. Scout time series extracted via the standardized low-resolution brain electromagnetic tomography (sLORETA) technique are utilized. The time series is converted to image representations using continuous wavelet transform (CWT) and fed as input to deep learning models. Two high-density EEG datasets are utilized to validate the efficacy of the proposed method: the online BrainLat dataset (128 channels, comprising 16 AD, 13 FTD, and 19 healthy controls (HC)) and the in-house IITD-AIIA dataset (64 channels, including subjects with 10 AD, 9 MCI, and 8 HC). Different classification strategies and classifier combinations have been utilized for the accurate mapping of classes in both data sets. The best results were achieved using a product of probabilities from classifiers for left and right subcortical regions in conjunction with the DenseNet model architecture. It yield accuracies of 94.17 % and 77.72 % on the BrainLat and IITD-AIIA datasets, respectively. The results highlight that the image representation-based deep learning approach has the potential to differentiate various stages of dementia. It pave the way for more accurate and early diagnosis, which is crucial for the effective treatment and management of debilitating conditions.

Constrained clustering problems generalize classical clustering formulations, e.g., $k$-median, $k$-means, by imposing additional constraints on the feasibility of clustering. There has been significant recent progress in obtaining approximation algorithms for these problems, both in the metric and the Euclidean settings. However, the outlier version of these problems, where the solution is allowed to leave out $m$ points from the clustering, is not well understood. In this work, we give a general framework for reducing the outlier version of a constrained $k$-median or $k$-means problem to the corresponding outlier-free version with only $(1+\varepsilon)$-loss in the approximation ratio. The reduction is obtained by mapping the original instance of the problem to $f(k,m, \varepsilon)$ instances of the outlier-free version, where $f(k, m, \varepsilon) = \left( \frac{k+m}{\varepsilon}\right)^{O(m)}$. As specific applications, we get the following results: - First FPT (in the parameters $k$ and $m$) $(1+\varepsilon)$-approximation algorithm for the outlier version of capacitated $k$-median and $k$-means in Euclidean spaces with hard capacities. - First FPT (in the parameters $k$ and $m$) $(3+\varepsilon)$ and $(9+\varepsilon)$ approximation algorithms for the outlier version of capacitated $k$-median and $k$-means, respectively, in general metric spaces with hard capacities. - First FPT (in the parameters $k$ and $m$) $(2-\delta)$-approximation algorithm for the outlier version of the $k$-median problem under the Ulam metric. Our work generalizes the known results to a larger class of constrained clustering problems. Further, our reduction works for arbitrary metric spaces and so can extend clustering algorithms for outlier-free versions in both Euclidean and arbitrary metric spaces.

Online convex paging (Menache and Singh, 2015; Chiplunkar, Henzinger, Kale, and Votsch, 2023) models a broad class of cost functions for the classical paging problem. In particular, it naturally captures fairness constraints: e.g., that no specific page (or groups of pages) suffers an "unfairly" high number of evictions by considering l.. norms of eviction vectors for p > 1. The case of the iota(infinity) norm has also been of special interest, and is called min-max paging. We give tight upper and lower bounds for the convex paging problem for a broad class of convex functions. Prior to our work, only fractional algorithms were known for this general setting. Moreover, our general result also improves on prior works for special cases of the problem. For example, it implies that the randomized competitive ratio of the min-max paging problem is Theta(log k log n); this improves both the upper bound and the lower bound given in prior work. It also shows that the randomized and deterministic competitive ratios for iota(p) -norm paging are Theta(p log k) and Theta(pk) respectively; the randomized results are completely new, as is the deterministic lower bound. All previous algorithms we know for paging with non-linear costs used fractional relaxations. We show a fundamental limitation of this approach - we give integrality gap instances for the natural relaxation used in these works. This shows that a generic relaxand-round framework-solving the relaxation and then rounding it-is insufficient for obtaining tight bounds for this problem. To bypass this bottleneck, we work with the integer versions of the problems directly. Somewhat surprisingly, we show how to take an arbitrary online algorithm for the weighted paging problem (with linear costs), and convert it in a black-box way to an online algorithm for convex paging, losing just an optimal factor in this reduction. This reduction proves especially challenging in the randomized case, where the underlying weighted paging algorithm is randomized, and the analysis needs to proceed via a delicate martingale argument. We believe this approach of lifting arbitrary (weighted linear) online algorithms to convex objectives may be of broader interest.

This study explores the effects of hydrogen addition on soot reduction in methane-air diffusion flames, employing computational analysis coupled with chemical equilibrium and k-epsilon combustion turbulence models. By varying the fuel mixture with hydrogen mass percentages ranging from 0% to 11%, alterations in flame behaviour were observed. Results revealed a notable increase in maximum flame temperature at 1.3% hydrogen addition, attributed to enhance combustion efficiency, while subsequent additions led to temperature decrements due to dilution effects. Concurrently, soot production exhibited a general decrease, with reductions quantified up to 96.7% compared to baseline conditions, primarily due to improved oxidation and decreased carbon content. Additionally, the position of maximum flame temperature and soot mass fraction shifted along the axial direction owing to hydrogen's higher flammability compared to methane-air diffusion. These findings offer insights into optimizing flame characteristics for reduced particulate matter emissions, emphasizing the potential of hydrogen addition in mitigating soot formation in diffusion flames.

Coresets for k-means and k-median problems yield a small summary of the data, which preserve the clustering cost with respect to any set of k centers. Recently coresets have also been constructed for constrained k-means and k-median problems. However, the notion of coresets has the drawback that (i) they can only be applied in settings where the input points are allowed to have weights, and (ii) in general metric spaces, the size of the coresets can depend logarithmically on the number of points. The notion of weak coresets, which have less stringent requirements than coresets, has been studied in the context of classical k-means and k-median problems. A weak coreset is a pair (J,S) of subsets of points, where S acts as a summary of the point set and J as a set of potential centers. This pair satisfies the properties that (i) S is a good summary of the data as long as the k centers are chosen from J only, and (ii) there is a good choice of k centers in J with cost close to the optimal cost. We develop this framework, which we call universal weak coresets, for constrained clustering settings. In conjunction with recent coreset constructions for constrained settings, our designs give greater data compression, are conceptually simpler, and apply to a wide range of constrained k-median and k-means problems.

This article presents a series of opposed flow flame spread experiments, conducted using cast cylindrical PMMA (acrylic) rods, 80 mm long and of diameters 1 mm and 0.5 mm, in normal gravity and microgravity environments. The experiments are primarily conducted for molar oxygen levels of 21 at 1 atmosphere pressure and opposed flow speed ranging from 0 cm/s to 25 cm/s. Experiments are also conducted in normal gravity for oxygen levels 21 to study the effect of oxygen level. At near ambient oxygen levels, the flame shape in microgravity resembles a mushroom and there are fluctuations at the leading edge due to sporadic fuel jets emanating from bursting bubbles at the fuel surface. The flame spreads faster in microgravity, which is determined to be due to increased preheat length. Preheat length is measured for flame spreading over 1 mm diameter fuel rod under no flow condition using fine thermocouples and is found to be 0.98 cm in microgravity and 0.34 cm in normal gravity. It is found that for scaling analysis, including Stefan flow velocity in the definition of reference velocity results in a reasonable estimate of the preheat length of a flame spreading in quiescent microgravity environment. At high oxygen levels (> 35 the same rate in normal gravity and microgravity environments and the flame spread rates are not affected by external flow speed.

In this work opposed flow flame spread over thin cellulosic circular ducts is investigated in normal gravity and microgravity environments for the first time. The experiments are conducted under different opposed flow speeds on circular ducts of diameter 10 mm, 19 mm and 38 mm and for comparison corresponding planar fuels of width of 10 mm, 20 mm and 40 mm are chosen respectively. All the microgravity tests are conducted using a 2.5 s drop tower facility. Over the matrix of test in the present study, the flame spread rates for circular ducts are higher compared to the planar fuel of corresponding widths. Unlike planar fuels where the effect of fuel width is small, the flame spread rate significantly increases with the increase in duct size in both normal gravity and micro-gravity. The flame spread rate over ducts exhibits a non-monotonic trend with flow speed which can also be seen in planar fuels. However, the variation with flow is much more significant especially at large diameters. The duct configuration also shows significant change in flame shape and size between normal gravity and micro-gravity environments. An analytical model is developed to predict flame spread rate over planar as well as circular ducts. The model successfully captures the flame spread rate trends with flow speed as well as fuel diameter.

We study the classical load balancing problem in a fully dynamic setting where jobs both arrive and depart. Each job can only be assigned to a subset of machines and can be reassigned at any time step. The goal is to maintain a near-optimal maximum load at all time steps with a small total number of reassignments. We consider the setting where the degree of the jobs (number of machines they can be assigned to) is bounded. This is motivated from natural settings where jobs can only be locally assigned to a small number of machines (e.g., bike sharing [10], map-reduce settings [21]) and generalizes the classical EdgeOrientation problem. We give a constant competitive algorithm with amortized constant number of reassignments. We also consider the generalizations of our problem to arbitrary reassignment costs and arbitrary job sizes. The generalizations require different techniques and we give a different randomized algorithm for these.

In order to achieve low cost and high efficiency with improved power quality at AC mains, a single stage bridgeless flyback (SSBL-Flyback) converter is used to drive the sensorless brushless direct current (BLDC) motor for the ceiling fan. In this, the conduction losses are reduced due to bridgeless configuration of the power factor corrected (PFC) converter. It is consisting of a dual flyback configuration, which provides good power quality indices at the AC mains. The PFC converter is designed in the discontinuous mode (DCM). The high frequency transformer provides the flexibility to improve the gain and design with lower voltage stress across the switch. The main aim of this paper is to eliminate all sensors including the PFC converter output DC link voltage sensor and reduce the overall cost of the BLDC motor ceiling fan with improved power quality at the AC input. An auxiliary winding voltage is used to take care of the input voltage variation and it is also utilized to control the PFC converter output voltage (DC link voltage) and correspondingly, ceiling fan speed is controlled. The voltage source inverter (VSI) is switched at fundamental frequency to reduce the switching losses in VSI. The behaviour of the ceiling fan is simulated in the MATLAB and shown in results section to validate the design.