Lower Bounds for Shoreline Searching With 2 or More Robots

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound known for $n=2$ robots from 1.5993 to 3. Moreover we prove that the competitive ratio is at least $\sqrt{3}$ for $n=3$ robots, and at least $1/\cos(\pi/n)$ for $n\geq 4$ robots. Our lower bounds match the best upper bounds known for $n\geq 4$, hence resolving these cases. To the best of our knowledge, these are the first lower bounds proven for the cases $n\geq 3$ of this several decades old problem.Comment: This is an updated version of the paper with the same title which will appear in the proceedings of the 23rd International Conference on Principles of Distributed Systems (OPODIS 2019) Neuchatel, Switzerland, July 17-19, 201

Digital Intensive Mixed Signal Circuits with In-situ Performance Monitors

University of Minnesota Ph.D. dissertation.November 2016. Major: Electrical/Computer Engineering. Advisor: Chris Kim. 1 computer file (PDF); x, 137 pages.Digital intensive circuit design techniques of different mixed-signal systems such as data converters, clock generators, voltage regulators etc. are gaining attention for the implementation of modern microprocessors and system-on-chips (SoCs) in order to fully utilize the benefits of CMOS technology scaling. Moreover different performance improvement schemes, for example, noise reduction, spur cancellation, linearity improvement etc. can be easily performed in digital domain. In addition to that, increasing speed and complexity of modern SoCs necessitate the requirement of in-situ measurement schemes, primarily for high volume testing. In-situ measurements not only obviate the need for expensive measurement equipments and probing techniques, but also reduce the test time significantly when a large number of chips are required to be tested. Several digital intensive circuit design techniques are proposed in this dissertation along with different in-situ performance monitors for a variety of mixed signal systems. First, a novel beat frequency quantization technique is proposed in a two-step VCO quantizer based ADC implementation for direct digital conversion of low amplitude bio- potential signals. By direct conversion, it alleviates the requirement of the area and power consuming analog-frontend (AFE) used in a conventional ADC designs. This prototype design is realized in a 65nm CMOS technology. Measured SNDR is 44.5dB from a 10mVpp, 300Hz signal and power consumption is only 38μW. Next, three different clock generation circuits, a phase-locked loop (PLL), a multiplying delay-locked loop (MDLL) and a frequency-locked loop (FLL) are presented. First a 0.4-to-1.6GHz sub-sampling fractional-N all digital PLL architecture is discussed that utilizes a D-flip-flop as a digital sub-sampler. Measurement results from a 65nm CMOS test-chip shows 5dB lower phase noise at 100KHz offset frequency, compared to a conventional architecture. The Digital PLL (DPLL) architecture is further extended for a digital MDLL implementation in order to suppress the VCO phase noise beyond the DPLL bandwidth. A zero-offset aperture phase detector (APD) and a digital- to-time converter (DTC) are employed for static phase-offset (SPO) cancellation. A unique in-situ detection circuitry achieves a high resolution SPO measurement in time domain. A 65nm test-chip shows 0.2-to-1.45GHz output frequency range while reducing the phase-noise by 9dB compared to a DPLL. Next, a frequency-to-current converter (FTC) based fractional FLL is proposed for a low accuracy clock generation in an extremely low area for IoT application. High density deep-trench capacitors are used for area reduction. The test-chip is fabricated in a 32nm SOI technology that takes only 0.0054mm2 active area. A high-resolution in-situ period jitter measurement block is also incorporated in this design. Finally, a time based digital low dropout (DLDO) regulator architecture is proposed for fine grain power delivery over a wide load current dynamic range and input/output voltage in order to facilitate dynamic voltage and frequency scaling (DVFS). High- resolution beat frequency detector dynamically adjusts the loop sampling frequency for ripple and settling time reduction due to load transients. A fixed steady-state voltage offset provides inherent active voltage positioning (AVP) for ripple reduction. Circuit simulations in a 65nm technology show more than 90% current efficiency for 100X load current variation, while it can operate for an input voltage range of 0.6V – 1.2V

The Fagnano Triangle Patrolling Problem

We investigate a combinatorial optimization problem that involves patrolling the edges of an acute triangle using a unit-speed agent. The goal is to minimize the maximum (1-gap) idle time of any edge, which is defined as the time gap between consecutive visits to that edge. This problem has roots in a centuries-old optimization problem posed by Fagnano in 1775, who sought to determine the inscribed triangle of an acute triangle with the minimum perimeter. It is well-known that the orthic triangle, giving rise to a periodic and cyclic trajectory obeying the laws of geometric optics, is the optimal solution to Fagnano's problem. Such trajectories are known as Fagnano orbits, or more generally as billiard trajectories. We demonstrate that the orthic triangle is also an optimal solution to the patrolling problem. Our main contributions pertain to new connections between billiard trajectories and optimal patrolling schedules in combinatorial optimization. In particular, as an artifact of our arguments, we introduce a novel 2-gap patrolling problem that seeks to minimize the visitation time of objects every three visits. We prove that there exist infinitely many well-structured billiard-type optimal trajectories for this problem, including the orthic trajectory, which has the special property of minimizing the visitation time gap between any two consecutively visited edges. Complementary to that, we also examine the cost of dynamic, sub-optimal trajectories to the 1-gap patrolling optimization problem. These trajectories result from a greedy algorithm and can be implemented by a computationally primitive mobile agent

Naphthoquinone-mediated inhibition of lysine acetyltransferase KAT3B/p300, basis for non-toxic inhibitor synthesis

Hydroxynaphthoquinone-based inhibitors of the lysine acetyltransferase KAT3B (p300), such as plumbagin, are relatively toxic. Here, we report that free thiol reactivity and redox cycling properties greatly contribute to the toxicity of plumbagin. A reactive 3rd position in the naphthoquinone derivatives is essential for thiol reactivity and enhances redox cycling. Using this clue, we synthesized PTK1, harboring a methyl substitution at the 3rd position of plumbagin. This molecule loses its thiol reactivity completely and its redox cycling ability to a lesser extent. Mechanistically, non-competitive, reversible binding of the inhibitor to the lysine acetyltransferase (KAT) domain of p300 is largely responsible for the acetyltransferase inhibition. Remarkably, the modified inhibitor PTK1 was a nearly non-toxic inhibitor of p300. The present report elucidates the mechanism of acetyltransferase activity inhibition by 1,4-naphthoquinones, which involves redox cycling and nucleophilic adduct formation, and it suggests possible routes of synthesis of the non-toxic inhibitor

Production of He-4 and (4) in Pb-Pb collisions at root(NN)-N-S=2.76 TeV at the LHC

Results on the production of He-4 and (4) nuclei in Pb-Pb collisions at root(NN)-N-S = 2.76 TeV in the rapidity range vertical bar y vertical bar <1, using the ALICE detector, are presented in this paper. The rapidity densities corresponding to 0-10% central events are found to be dN/dy4(He) = (0.8 +/- 0.4 (stat) +/- 0.3 (syst)) x 10(-6) and dN/dy4 = (1.1 +/- 0.4 (stat) +/- 0.2 (syst)) x 10(-6), respectively. This is in agreement with the statistical thermal model expectation assuming the same chemical freeze-out temperature (T-chem = 156 MeV) as for light hadrons. The measured ratio of (4)/He-4 is 1.4 +/- 0.8 (stat) +/- 0.5 (syst). (C) 2018 Published by Elsevier B.V.Peer reviewe

Influence of slip velocity at the core of a diffuse soft particle and ion partition effects on mobility

Nonlinear effects on the electrophoresis of a soft particle, consisting of a rigid hydrophobic core coated with a diffuse polymer layer (PEL) suspended in an electrolyte medium, are studied. The impact of the ion partitioning effect arising due to the Born energy difference between the PEL and the electrolyte is approximated based on the equilibrium Boltzmann equation, with which the ion distribution and hence, the charge density is modified. The equations describing the electrokinetic transport comprising the Darcy-Brinkman extended Navier-Stokes equations which includes the ion partitioning effect coupled with the modified Nernst-Planck equations and Poisson equations for electric field are solved numerically. The present numerical model for the soft particle compares well with the existing theoretical solutions and experimental results in the limiting cases. A deviation from existing simplified models based on the Boltzmann distribution of ions occurs when the Debye layer polarization, relaxation and the electroosmosis induced by the PEL immobile charge become significant. The hydrophobicity of the inner core strongly influences the nonlinear electrokinetic effects by modifying the Debye layer, electroosmotic flow in the PEL and surface conduction. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of the soft particle by attenuating the shielding effect. When the Debye layer is in the order of the particle size the hydrophobicity of the core surface and the ion partitioning effect manifest the surface conduction, which implies that the Boltzmann distribution of ions is no longer valid. The core hydrophobicity and ion partitioning effect have influence on the condensation of the PEL immobile charge, which creates a significant impact on the mobility

Finitely chainable and totally bounded metric spaces: Equivalent characterizations

A metric space (X, d) is called finitely chainable if for every epsilon > 0, there are finitely many points p(1), p(2),..., p(r) in X and a positive integer m such that every point of X can be joined with some p(j), 1 <= j <= r by an epsilon-chain of length m. In 1958, Atsuji proved: a metric space (X, d) is finitely chainable if and only if every real valued uniformly continuous function on (X, d) is bounded. In this paper, we study twenty-five equivalent characterizations of finitely chainable metric spaces, out of which three are entirely new. Here we would like to mention that this study essentially turns the first part of this paper into a sort of an expository research article. A totally bounded metric space is finitely chainable. In order to have a better perception of the difference between total boundedness and finite chainability, several new equivalent characterizations of totally bounded metric spaces are also studied. Moreover, two topological characterizations of metric spaces admitting compatible finitely chainable metrics are given. (C) 2016 Elsevier B.V. All rights reserved

Viewing global strategy through a microfoundations lens

Research Summary: The emerging microfoundations literature asserts that macro concepts and macro-out-comes, such as firm-level capabilities, performance and strategies, need to be understood in terms of the underlying actions, interactions and characteristics of micro-level entities, such as individual actors and managers. This literature has specific implications for the understanding of cross-level explanatory mechanisms; notably, it asserts that all relations between macro variables are mechanisms that involve micro variables. While the microfoundations literature has been influential in the general strategy literature, global strategy has been less impacted by it. This is paradoxical because the research challenges pointed to by the literature are often magnified in the multinational corporation and in a global strategy context, and this context may introduce novel challenges. For example, Google's strategic decision in 2018 to reenter the Chinese market (macro-level analysis) is best understood through the thinking of decision-makers in the company, as well as opposition to the move from over 1,000 of its employees. We characterize microfoundations, discuss their relevance to the global strategy, and show how the papers in this special issue fill important microfoundational gaps in the global strategy literature. Managerial Summary: For too long, studies of corporate strategies have focused on the firm as a unit of analysis, as if the firm could decide or think on its own, neglecting the fact that it is managers who think. The underlying motivations, interactions and characteristics of individual managers of companies have often been missing in explanations of global strategy formulation. This can especially be a lacuna in closely-held companies in emerging countries where decision-making is more concentrated in the minds of owners, top managers and family members. The microfoundations literature specifically tries to connect the thinking and backgrounds of individual managers with strategic decisions their firm makes. While the microfoundations literature has made some headway in the general strategy literature, the analysis of global strategy has been less impacted by it. This is paradoxical because the research challenges pointed to by the literature are often magnified in the multinational corporation and in a global strategy context. This introductory paper first refines and enunciates microfoundations theory, in its application to global business. It then also shows how the papers in this special issue fill important microfoundational gaps in the global strategy literature