Changing Bases: Multistage Optimization for Matroids and Matchings

This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems, without creating too much churn in the solution itself. We model this as a multistage combinatorial optimization problem where the input is a sequence of cost functions (one for each time step); while we can change the solution from step to step, we incur an additional cost for every such change. We study the multistage matroid maintenance problem, where we need to maintain a base of a matroid in each time step under the changing cost functions and acquisition costs for adding new elements. The online version of this problem generalizes online paging. E.g., given a graph, we need to maintain a spanning tree $T_t$ at each step: we pay $c_t(T_t)$ for the cost of the tree at time $t$, and also $| T_t\setminus T_{t-1} |$ for the number of edges changed at this step. Our main result is an $O(\log m \log r)$-approximation, where $m$ is the number of elements/edges and $r$ is the rank of the matroid. We also give an $O(\log m)$ approximation for the offline version of the problem. These bounds hold when the acquisition costs are non-uniform, in which caseboth these results are the best possible unless P=NP. We also study the perfect matching version of the problem, where we must maintain a perfect matching at each step under changing cost functions and costs for adding new elements. Surprisingly, the hardness drastically increases: for any constant $\epsilon>0$, there is no $O(n^{1-\epsilon})$-approximation to the multistage matching maintenance problem, even in the offline case

Thin front propagation in random shear flows

Front propagation in time dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts, i.e. the so-called geometrical optics limit. In particular, we consider fronts evolving in time correlated random shear flows, modeled in terms of Ornstein-Uhlembeck processes. We show that the ratio between the time correlation of the flow and an intrinsic time scale of the reaction dynamics (the wrinkling time $t_w$) is crucial in determining both the front propagation speed and the front spatial patterns. The relevance of time correlation in realistic flows is briefly discussed in the light of the bending phenomenon, i.e. the decrease of propagation speed observed at high flow intensities.Comment: 5 Revtex4 pages, 4 figures include

Online unit clustering in higher dimensions

We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of $n$ points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into the minimum number of clusters (subsets) of diameter at most one; while Unit Covering asks to cover all points by the minimum number of balls of unit radius. In this paper, we work in $\mathbb{R}^d$ using the $L_\infty$ norm. We show that the competitive ratio of any online algorithm (deterministic or randomized) for Unit Clustering must depend on the dimension $d$. We also give a randomized online algorithm with competitive ratio $O(d^2)$ for Unit Clustering}of integer points (i.e., points in $\mathbb{Z}^d$, $d\in \mathbb{N}$, under $L_{\infty}$ norm). We show that the competitive ratio of any deterministic online algorithm for Unit Covering is at least $2^d$. This ratio is the best possible, as it can be attained by a simple deterministic algorithm that assigns points to a predefined set of unit cubes. We complement these results with some additional lower bounds for related problems in higher dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA 2017

Thermoelectric Amplification of Phonons in Graphene

Amplification of acoustic phonons due to an external temperature gredient ($\nabla T$) in Graphene was studied theoretically. The threshold temperature gradient $(\nabla T)_0^{g}$ at which absorption switches over to amplification in Graphene was evaluated at various frequencies $\omega_q$ and temperatures $T$. For $T = 77K$ and frequency $\omega_q = 12THz$, $(\nabla T)_0^{g} = 0.37Km^{-1}$. The calculation was done in the regime at $ql >> 1$. The dependence of the normalized ($\Gamma/\Gamma_0$) on the frequency $\omega_q$ and the temperature gradient $(\nabla T/T)$ are evaluated numerically and presented graphically. The calculated $(\nabla T)_0^{g}$ for Graphene is lower than that obtained for homogeneous semiconductors ($n-InSb$) $(\nabla T)_0^{hom} \approx 10^3Kcm^{-1}$, Superlattices $(\nabla T)_0^{SL} = 384Kcm^{-1}$, Cylindrical Quantum Wire $(\nabla T)_0^{cqw} \approx 10^2Kcm^{-1}$. This makes Graphene a much better material for thermoelectric phonon amplifier.Comment: 12 Pages, 6 figure

Cats with thermal burn injuries from California wildfires show echocardiographic evidence of myocardial thickening and intracardiac thrombi.

Recent increases in the prevalence and severity of wildfires in some regions have resulted in an increased frequency of veterinary burn patients. Few studies exist regarding diagnostics and management of burn wounds in veterinary patients and current knowledge is extrapolated from human literature and research models. Post-burn cardiac injury is a common finding and predictor of mortality in human patients and echocardiography is an important tool in monitoring response to therapy and predicting outcome. We describe the notable findings from cats naturally exposed to California wildfires in 2017 and 2018. Domestic cats (n = 51) sustaining burn injuries from the Tubbs (2017) and Camp (2018) wildfires were prospectively enrolled and serial echocardiograms and cardiac troponin I evaluations were performed. Echocardiograms of affected cats revealed a high prevalence of myocardial thickening (18/51) and spontaneous echocardiographic contrast and thrombi formation (16/51). Forty-two cats survived to discharge and 6 died or were euthanized due to a possible cardiac cause. For the first time, we describe cardiovascular and coagulation effects of thermal burn and smoke inhalation in cats. Further studies in veterinary burn victims are warranted and serve as a translational research opportunity for uncovering novel disease mechanisms and therapies

EXPERIMENTS AND MODELLING OF CALCIUM SULPHATE PRECIPITATION UNDER SENSIBLE HEATING CONDITIONS: INITIAL FOULING AND BULK PRECIPITATION RATE STUDIES

Crystallization of calcium sulphate, an inverse solubility salt, on a heated surface under sensible heating conditions has been studied. A temperature measurement technique was employed to detect initial fouling rates. Fouling experiments were carried out to determine how process variables such as surface temperature and velocity affect the initial fouling rates of calcium sulphate scaling. Experimental results show that, at a given surface temperature, there exists a maximum initial fouling rate for a range of fluid velocities. Also, this maximum rate and the fluid velocity at which it occurs both increase as the surface temperature increases. These observations are all qualitatively in agreement with the Initial Fouling Rate Model (IFRM) of Epstein (1994). The fouling experiments were supplemented by kinetic batch experiments to make a comparison between fouling activation energies and purely chemical activation energies

Lower bounds for several online variants of bin packing

We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201

Hyperglycemia alters enzyme activity and cell number in spinal sensory ganglia

Peripheral sensory diabetic neuropathy is characterized by morphological, electrophysiological and neurochemical changes to a subpopulation of primary afferent neurons. Here, we utilized a transgenic mouse model of diabetes (OVE26) and age-matched controls to histologically examine the effect of chronic hyperglycemia on the activity or abundance of the enzymes acid phosphatase, cytochrome oxidase and NADPH-diaphorase in primary sensory neuron perikarya and the dorsal horn of the spinal cord. Quantitative densitometric characterization of enzyme reaction product revealed significant differences between diabetic, compared to control, animals for all three enzymes. Levels of acid phosphatase reaction product were found to be significantly reduced in both small diameter primary sensory somata and the dorsal horn. Cytochrome oxidase activity was found to be significantly lower in small primary sensory somata while NADPH-diaphorase labeling was found to be significantly higher in small primary sensory somata and significantly lower in the dorsal horn. In addition to these observed biochemical changes, ratiometric analysis of the number of small versus large diameter primary sensory perikarya in diabetic and control animals demonstrated a quantifiable decrease in the number of small diameter cells in the spinal ganglia of diabetic mice. These results suggest that the OVE26 model of diabetes mellitus produces an identifiable disturbance in specific metabolic pathways of select cells in the sensory nervous system and that this dysfunction may reflect the progression of a demonstrated cell loss