Matrix model holography

We set up the formalism of holographic renormalization for the matter-coupled two-dimensional maximal supergravity that captures the low-lying fluctuations around the non-conformal D0-brane near-horizon geometry. As an application we compute holographically one- and two-point functions of the BFSS matrix quantum mechanics and its supersymmetric $SO(3)\times SO(6)$ deformation.Comment: 30 pages, 1 figure; v2: ten-dimensional interpretation of the deformed solution as the near-horizon limit of a distribution of D0 branes; version to appear in JHE

Clustered Star Formation in the Small Magellanic Cloud. A Spitzer/IRAC View of the Star-Forming Region NGC 602/N 90

We present Spitzer/IRAC photometry on the star-forming HII region N 90, related to the young stellar association NGC 602 in the Small Magellanic Cloud. Our photometry revealed bright mid-infrared sources, which we classify with the use of a scheme based on templates and models of red sources in the Milky Way, and criteria recently developed from the Spitzer Survey of the SMC for the selection of candidate Young Stellar Objects (YSOs). We detected 57 sources in all four IRAC channels in a 6.2' x 4.8' field-of-view centered on N 90; 22 of these sources are classified as candidate YSOs. We compare the locations of these objects with the position of optical sources recently found in the same region with high-resolution HST/ACS imaging of NGC 602, and we find that 17 candidate YSOs have one or more optical counterparts. All of these optical sources are identified as pre-main sequence stars, indicating, thus, ongoing clustered star formation events in the region. The positions of the detected YSOs and their related PMS clusters give a clear picture of the current star formation in N 90, according to which the young stellar association photo-ionizes the surrounding interstellar medium, revealing the HII nebula, and triggering sequential star formation events mainly along the eastern and southern rims of the formed cavity of the parental molecular cloud.Comment: Accepted fro Publication in ApJ. 8 pages, 6 figures, 3 color figures submitted as JP

Terahertz Magnetoplasmon Energy Concentration and Splitting in Graphene PN Junctions

Terahertz plasmons and magnetoplasmons propagating along electrically and chemically doped graphene p-n junctions are investigated. It is shown that such junctions support non-reciprocal magnetoplasmonic modes which get concentrated at the middle of the junction in one direction and split away from the middle of the junction in the other direction under the application of an external static magnetic field. This phenomenon follows from the combined effects of circular birefringence and carrier density non-uniformity. It can be exploited for the realization of plasmonic isolators.Comment: 6 Pages, 10 figure

Geometries of third-row transition-metal complexes from density-functional theory

A set of 41 metal-ligand bond distances in 25 third-row transition-metal complexes, for which precise structural data are known in the gas phase, is used to assess optimized and zero-point averaged geometries obtained from DFT computations with various exchange-correlation functionals and basis sets. For a given functional (except LSDA) Stuttgart-type quasi-relativistic effective core potentials and an all-electron scalar relativistic approach (ZORA) tend to produce very similar geometries. In contrast to the lighter congeners, LSDA affords reasonably accurate geometries of 5d-metal complexes, as it is among the functionals with the lowest mean and standard deviations from experiment. For this set the ranking of some other popular density functionals, ordered according to decreasing standard deviation, is BLYP > VSXC > BP86 approximate to BPW91 approximate to TPSS approximate to B3LYP approximate to PBE > TPSSh > B3PW91 approximate to B3P86 approximate to PBE hybrid. In this case hybrid functionals are superior to their nonhybrid variants. In addition, we have reinvestigated the previous test sets for 3d- (Buhl M.; Kabrede, H. J. Chem. Theory Comput. 2006, 2, 1282-1290) and 4d- (Waller, M. P.; Buhl, M. J. Comput. Chem. 2007,28,1531-1537) transition-metal complexes using all-electron scalar relativistic DFT calculations in addition to the published nonrelativistic and ECP results. For this combined test set comprising first-, second-, and third-row metal complexes, B3P86 and PBE hybrid are indicated to perform best. A remarkably consistent standard deviation of around 2 pm in metal-ligand bond distances is achieved over the entire set of d-block elements.PostprintPeer reviewe

Balanced Allocations in Batches: The Tower of Two Choices

In balanced allocations, the goal is to place $m$ balls into $n$ bins, so as to minimize the gap (difference of max to average load). The One-Choice process places each ball to a bin sampled independently and uniformly at random. The Two-Choice process places balls in the least loaded of two sampled bins. Finally, the $(1+\beta)$-process mixes these processes, meaning each ball is allocated using Two-Choice with probability $\beta\in(0,1)$, and using One-Choice otherwise. Despite Two-Choice being optimal in the sequential setting, it has been observed in practice that it does not perform well in a parallel environment, where load information may be outdated. Following [BCEFN12], we study such a parallel setting where balls are allocated in batches of size $b$, and balls within the same batch are allocated with the same strategy and based on the same load information. For small batch sizes $b\in[n,n\log n]$, it was shown in [LS22a] that Two-Choice achieves an asymptotically optimal gap among all processes with a constant number of samples. In this work, we focus on larger batch sizes $b\in[n\log n,n^3]$. It was proved in [LS22c] that Two-Choice leads to a gap of $\Theta(b/n)$. As our main result, we prove that the gap reduces to $O(\sqrt{(b/n)\cdot\log n})$, if one runs the $(1+\beta)$-process with an appropriately chosen $\beta$ (in fact this result holds for a larger class of processes). This not only proves the phenomenon that Two-Choice is not the best (leading to the formation of "towers" over previously light bins), but also that mixing two processes (One-Choice and Two-Choice) leads to a process which achieves a gap that is asymptotically smaller than both. We also derive a matching lower bound of $\Omega(\sqrt{(b/n)\cdot\log n})$ for any allocation process, which demonstrates that the above $(1+\beta)$-process is asymptotically optimal.Comment: 36 pages;6 figures; 2 tables. arXiv admin note: text overlap with arXiv:2203.1390

An Improved Drift Theorem for Balanced Allocations

In the balanced allocations framework, there are $m$ jobs (balls) to be allocated to $n$ servers (bins). The goal is to minimize the gap, the difference between the maximum and the average load. Peres, Talwar and Wieder (RSA 2015) used the hyperbolic cosine potential function to analyze a large family of allocation processes including the $(1+\beta)$-process and graphical balanced allocations. The key ingredient was to prove that the potential drops in every step, i.e., a drift inequality. In this work we improve the drift inequality so that (i) it is asymptotically tighter, (ii) it assumes weaker preconditions, (iii) it applies not only to processes allocating to more than one bin in a single step and (iv) to processes allocating a varying number of balls depending on the sampled bin. Our applications include the processes of (RSA 2015), but also several new processes, and we believe that our techniques may lead to further results in future work.Comment: This paper refines and extends the content on the drift theorem and applications in arXiv:2203.13902. It consists of 38 pages, 7 figures, 1 tabl

Modeling and Design of High-Performance DC-DC Converters

The goal of the research that was pursued during this PhD is to eventually facilitate the development of high-performance, fast-switching DC-DC converters. High-switching frequency in switching mode power supplies (SMPS) can be exploited by reducing the output voltage ripple for the same size of passives (mainly inductors and capacitors) and improve overall system performance by providing a voltage supply with less unwanted harmonics to the subsystems that they support. The opposite side of the trade-off is also attractive for designers as the same amount of ripple can be achieved with smaller values of inductance and/or capacitance which can result in a physically smaller and potentially cheaper end product. Another benefit is that the spectrum of the resulting switching noise is shifted to higher frequencies which in turn allows designers to push the corner frequency of the control loop of the system higher without the switching noise affecting the behavior of the system. This in turn, is translated to a system capable of responding faster to strong transients that are common in modern systems that may contain microprocessors or other electronics that tend to consume power in bursts and may even require the use of features like dynamic voltage scaling to minimize the overall consumption of the system. While the analysis of the open loop behavior of a DC-DC converter is relatively straightforward, it is of limited usefulness as they almost always operate in closed loop and therefore can suffer from degraded stability. Therefore, it is important to have a way to simulate their closed loop behavior in the most efficient manner possible. The first chapter is dedicated to a library of technology-agnostic high-level models that can be used to improve the efficiency of transient simulations without sacrificing the ability to model and localize the different losses. This work also focuses further in fixed-frequency converters that employ Peak Current Mode Control (PCM) schemes. PCM schemes are frequently used due to their simple implementation and their ability to respond quickly to line transients since any change of the battery voltage is reflected in the slope of the rising inductor current which in turn is monitored by a fast internal control loop that is closed with the help of a current sensor. Most existing models for current sensors assume that they behave in an ideal manner with infinite bandwidth and ideal constant gain. These assumptions tend to be in significant error as the minimum on-time of the sensor and therefore the settling time requirements of the sensor are reduced. Some sensing architectures, like the ones that approximate the inductor current with the high-side switch current, can be even more complex to analyze as they require the use of extended masking time to prevent spike currents caused by the switch commutation to be injected to the output of the sensor and therefore the signal processing blocks of the control loop. In order to solve this issue, this work also proposes a current sensor model that is compatible with time averaged models of DC-DC converters and is able to predict the effects of static and transient non-idealities of the block on the behavior of a PCM DC-DC converter. Lastly, this work proposes a new 40 V, 6 A, fully-integrated, high-side current sensing circuit with a response time of 51 . The proposed sensor is able to achieve this performance with the help of a feedback resistance emulation technique that prevents the sensor from debiasing during its masking phase which tends to extend the response time of similar fully integrated sensors

Weighted Sampling for Combined Model Selection and Hyperparameter Tuning

The combined algorithm selection and hyperparameter tuning (CASH) problem is characterized by large hierarchical hyperparameter spaces. Model-free hyperparameter tuning methods can explore such large spaces efficiently since they are highly parallelizable across multiple machines. When no prior knowledge or meta-data exists to boost their performance, these methods commonly sample random configurations following a uniform distribution. In this work, we propose a novel sampling distribution as an alternative to uniform sampling and prove theoretically that it has a better chance of finding the best configuration in a worst-case setting. In order to compare competing methods rigorously in an experimental setting, one must perform statistical hypothesis testing. We show that there is little-to-no agreement in the automated machine learning literature regarding which methods should be used. We contrast this disparity with the methods recommended by the broader statistics literature, and identify a suitable approach. We then select three popular model-free solutions to CASH and evaluate their performance, with uniform sampling as well as the proposed sampling scheme, across 67 datasets from the OpenML platform. We investigate the trade-off between exploration and exploitation across the three algorithms, and verify empirically that the proposed sampling distribution improves performance in all cases.Comment: Accepted for presentation at The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI 2020