Balanced Allocation on Graphs: A Random Walk Approach

In this paper we propose algorithms for allocating $n$ sequential balls into $n$ bins that are interconnected as a $d$-regular $n$-vertex graph $G$, where $d\ge3$ can be any integer.Let $l$ be a given positive integer. In each round $t$, $1\le t\le n$, ball $t$ picks a node of $G$ uniformly at random and performs a non-backtracking random walk of length $l$ from the chosen node.Then it allocates itself on one of the visited nodes with minimum load (ties are broken uniformly at random). Suppose that $G$ has a sufficiently large girth and $d=\omega(\log n)$. Then we establish an upper bound for the maximum number of balls at any bin after allocating $n$ balls by the algorithm, called {\it maximum load}, in terms of $l$ with high probability. We also show that the upper bound is at most an $O(\log\log n)$ factor above the lower bound that is proved for the algorithm. In particular, we show that if we set $l=\lfloor(\log n)^{\frac{1+\epsilon}{2}}\rfloor$, for every constant $\epsilon\in (0, 1)$, and $G$ has girth at least $\omega(l)$, then the maximum load attained by the algorithm is bounded by $O(1/\epsilon)$ with high probability.Finally, we slightly modify the algorithm to have similar results for balanced allocation on $d$-regular graph with $d\in[3, O(\log n)]$ and sufficiently large girth

EVALUATION OF THE ANTIOXIDANT ACTIVITY OF THE FLAVONOIDS ISOLATED FROM HELIOTROPIUM SINUATUM RESIN USING ORACFL, DPPH AND ESR METHODOLOGIES

Indexación: Web of Science; Scielo.The antioxidant capacity has been determined for a number of flavonoid compounds from Heliotropium sinuatum, a plant that grows in arid areas in the north of Chile. The methodologies used were: ORAC(FL) (oxygen radical absorbance capacity - fluorescein), DPPH (2,2-diphenyl-2-picrylhydrazyl) bleaching and electron spin resonance (ESR). These compounds were studied in homogeneous and heterogeneous media. The results showed that the 7-o-methyleriodictiol and 3-o-methylisorhamnetin are those with the highest antioxidant capacity.http://ref.scielo.org/m82cz

Modeling of a Cantilever-Based Near-Field Scanning Microwave Microscope

We present a detailed modeling and characterization of our scalable microwave nanoprobe, which is a micro-fabricated cantilever-based scanning microwave probe with separated excitation and sensing electrodes. Using finite-element analysis, the tip-sample interaction is modeled as small impedance changes between the tip electrode and the ground at our working frequencies near 1GHz. The equivalent lumped elements of the cantilever can be determined by transmission line simulation of the matching network, which routes the cantilever signals to 50 Ohm feed lines. In the microwave electronics, the background common-mode signal is cancelled before the amplifier stage so that high sensitivity (below 1 atto-Farad capacitance changes) is obtained. Experimental characterization of the microwave probes was performed on ion-implanted Si wafers and patterned semiconductor samples. Pure electrical or topographical signals can be realized using different reflection modes of the probe.Comment: 7 figure

A Supercooled Spin Liquid State in the Frustrated Pyrochlore Dy2Ti2O7

A "supercooled" liquid develops when a fluid does not crystallize upon cooling below its ordering temperature. Instead, the microscopic relaxation times diverge so rapidly that, upon further cooling, equilibration eventually becomes impossible and glass formation occurs. Classic supercooled liquids exhibit specific identifiers including microscopic relaxation times diverging on a Vogel-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function, and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation. Recently, the pyrochlore Dy2Ti2O7 has become of interest because its frustrated magnetic interactions may, in theory, lead to highly exotic magnetic fluids. However, its true magnetic state at low temperatures has proven very difficult to identify unambiguously. Here we introduce high-precision, boundary-free magnetization transport techniques based upon toroidal geometries and gain a fundamentally new understanding of the time- and frequency-dependent magnetization dynamics of Dy2Ti2O7. We demonstrate a virtually universal HN form for the magnetic susceptibility, a general KWW form for the real-time magnetic relaxation, and a divergence of the microscopic magnetic relaxation rates with precisely the VTF trajectory. Low temperature Dy2Ti2O7 therefore exhibits the characteristics of a supercooled magnetic liquid; the consequent implication is that this translationally invariant lattice of strongly correlated spins is evolving towards an unprecedented magnetic glass state, perhaps due to many-body localization of spin.Comment: Version 2 updates: added legend for data in Figures 4A and 4B; corrected equation reference in caption for Figure 4

Statistical mechanics of budget-constrained auctions

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.Comment: Minor revisio

The power of choice in network growth

The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen contacts, where k > 1 is a constant. It then attaches to whichever one of these contacts is most desirable in some sense, such as its distance from the root or its degree. Even when the new node has just two choices, i.e., when k=2, the resulting network can be very different from a random graph or tree. For instance, if the new node attaches to the contact which is closest to the root of the tree, the distribution of depths changes from Poisson to a traveling wave solution. If the new node attaches to the contact with the smallest degree, the degree distribution is closer to uniform than in a random graph, so that with high probability there are no nodes in the network with degree greater than O(log log N). Finally, if the new node attaches to the contact with the largest degree, we find that the degree distribution is a power law with exponent -1 up to degrees roughly equal to k, with an exponential cutoff beyond that; thus, in this case, we need k >> 1 to see a power law over a wide range of degrees.Comment: 9 pages, 4 figure

Global Ultrasound Elastography Using Convolutional Neural Network

Displacement estimation is very important in ultrasound elastography and failing to estimate displacement correctly results in failure in generating strain images. As conventional ultrasound elastography techniques suffer from decorrelation noise, they are prone to fail in estimating displacement between echo signals obtained during tissue distortions. This study proposes a novel elastography technique which addresses the decorrelation in estimating displacement field. We call our method GLUENet (GLobal Ultrasound Elastography Network) which uses deep Convolutional Neural Network (CNN) to get a coarse time-delay estimation between two ultrasound images. This displacement is later used for formulating a nonlinear cost function which incorporates similarity of RF data intensity and prior information of estimated displacement. By optimizing this cost function, we calculate the finer displacement by exploiting all the information of all the samples of RF data simultaneously. The Contrast to Noise Ratio (CNR) and Signal to Noise Ratio (SNR) of the strain images from our technique is very much close to that of strain images from GLUE. While most elastography algorithms are sensitive to parameter tuning, our robust algorithm is substantially less sensitive to parameter tuning.Comment: 4 pages, 4 figures; added acknowledgment section, submission type late

Managing Climate Risk

At the heart of the traditional approach to strategy in the climate change dilemma lies the assumption that the global community, by applying a set of powerful analytical tools, can predict the future of climate change accurately enough to choose a clear strategic direction for it. We claim that this approach might involve underestimating uncertainty in order to lay out a vision of future events sufficiently precise to be captured in a discounted cost flow analysis in integrated assessment models. However, since the future of climate change is truly uncertain, this approach might at best be marginally helpful and at worst downright dangerous: underestimating uncertainty can lead to strategies that do not defend the world against unexpected and sometimes even catastrophic threats. Another danger lies on the other extreme: if the global community can not find a strategy that works under traditional analysis or if uncertainties are too large that clear messages are absent, they may abandon the analytical rigor of their planning process altogether and base their decisions on good instinct and consensus of some future process that is easy to agree upon. In this paper, we try to outline a system to derive strategic decisions under uncertainty for the climate change dilemma. What follows is a framework for determining the level of uncertainty surrounding strategic decisions and for tailoring strategy to that uncertainty. Our core argument is that a robust strategy towards climate change involves the building of a technological portfolio of mitigation and adaptation measures that includes sufficient opposite technological positions to the underlying baseline emission scenarios given the uncertainties of the entire physical and socioeconomic system in place. In the case of mitigation, opposite technological positions with the highest leverage are particular types of sinks. A robust climate risk management portfolio can only work when the opposite technological positions are readily available when needed and therefore have to be prepared in advance. It is precisely the flexibility of these technological options which has to be quantified under the perspective of the uncertain nature of the underlying system and compared to the cost of creating these options, rather than comparing their cost with expected losses in a net present value type analysis. We conclude that climate policy - especially under the consideration of the precautionary principle - would look much different if uncertainties would be taken explicitly into account

Nutrientes de cultivares de Cynodon, em duas épocas do ano, no Estado do Piauí.

Avaliaram-se os teores de proteína bruta, cálcio e fósforo em oito cultivares de cynodon: C. dactylon (L.) Pers. var. Aridus cv. Callie, C. dactylon (L.) Pers. cv. Coastcross, C. nlemfuensis Vanderyst cv. Estrela africana..

New and revised maimetshid wasps from cretaceous ambers (Hymenoptera, Maimetshidae)

New material of the wasp family Maimetshidae (Apocrita) is presented from four Cretaceous amber de- posits- the Neocomian of Lebanon, the Early Albian of Spain, the latest Albian/earliest Cenomanian of France, and the Campanian of Canada. The new record from Canadian Cretaceous amber extends the temporal and paleogeographical range of the family. New material from France is assignable to Guyote- maimetsha enigmatica Perrichot et al. including the first females for the species, while a series of males and females from Spain are described and figured as Iberomaimetsha Ortega-Blanco, Perrichot & Engel, gen. n., with the two new species Iberomaimetsha rasnitsyni Ortega-Blanco, Perrichot & Engel, sp. n. and I. nihtmara Ortega-Blanco, Delclòs & Engel, sp. n.; a single female from Lebanon is described and figured as Ahiromaimetsha najlae Perrichot, Azar, Nel & Engel, gen. et sp. n., and a single male from Canada is described and figured as Ahstemiam cellula McKellar & Engel, gen. et sp. n. The taxa are compared with other maimetshids, a key to genera and species is given, and brief comments made on the family