Intermediate problems in modular circuits satisfiability

In arXiv:1710.08163 a generalization of Boolean circuits to arbitrary finite algebras had been introduced and applied to sketch P versus NP-complete borderline for circuits satisfiability over algebras from congruence modular varieties. However the problem for nilpotent (which had not been shown to be NP-hard) but not supernilpotent algebras (which had been shown to be polynomial time) remained open. In this paper we provide a broad class of examples, lying in this grey area, and show that, under the Exponential Time Hypothesis and Strong Exponential Size Hypothesis (saying that Boolean circuits need exponentially many modular counting gates to produce boolean conjunctions of any arity), satisfiability over these algebras have intermediate complexity between $\Omega(2^{c\log^{h-1} n})$ and $O(2^{c\log^h n})$, where $h$ measures how much a nilpotent algebra fails to be supernilpotent. We also sketch how these examples could be used as paradigms to fill the nilpotent versus supernilpotent gap in general. Our examples are striking in view of the natural strong connections between circuits satisfiability and Constraint Satisfaction Problem for which the dichotomy had been shown by Bulatov and Zhuk

The physics of snow crystals

We examine the physical mechanisms governing the formation of snow crystals, treating this problem as a case study of the dynamics of crystal growth from the vapour phase. Particular attention is given to the basic theoretical underpinnings of the subject, especially the interplay of particle diffusion, heat diffusion and surface attachment kinetics during crystal growth, as well as growth instabilities that have important effects on snow crystal development. The first part of this review focuses on understanding the dramatic variations seen in snow crystal morphology as a function of temperature, a mystery that has remained largely unsolved since its discovery 75 years ago. To this end we examine the growth of simple hexagonal ice prisms in considerable detail, comparing crystal growth theory with laboratory measurements of growth rates under a broad range of conditions. This turns out to be a surprisingly rich problem, which ultimately originates from the unusual molecular structure of the ice surface and its sensitive dependence on temperature. With new clues from precision measurements of attachment kinetics, we are now just beginning to understand these structural changes at the ice surface and how they affect the crystal growth process. We also touch upon the mostly unexplored topic of how dilute chemical impurities can greatly alter the growth of snow crystals. The second part of this review examines pattern formation in snow crystals, with special emphasis on the growth of snow crystal dendrites. Again we treat this as a case study of the more general problem of dendritic growth during diffusion-limited solidification. Since snow crystals grow from the vapour, we can apply dendrite theory in the simplified slow-growth limit where attachment kinetics dominates over capillarity in selecting the tip velocity. Although faceting is quite pronounced in these structures, many aspects of the formation of snow crystal dendrites are fairly well described using a theoretical treatment that does not explicitly incorporate faceting. We also describe electrically modified ice dendrite growth, which produces some novel needle-like structures

Design of a High Capacity, Scalable, and Green Wireless Communication System Leveraging the Unlicensed Spectrum

The stunning demand for mobile wireless data that has been recently growing at an exponential rate requires a several fold increase in spectrum. The use of unlicensed spectrum is thus critically needed to aid the existing licensed spectrum to meet such a huge mobile wireless data traffic growth demand in a cost effective manner. The deployment of Long Term Evolution (LTE) in the unlicensed spectrum (LTE-U) has recently been gaining significant industry momentum. The lower transmit power regulation of the unlicensed spectrum makes LTE deployment in the unlicensed spectrum suitable only for a small cell. A small cell utilizing LTE-L (LTE in licensed spectrum), and LTE-U (LTE in unlicensed spectrum) will therefore significantly reduce the total cost of ownership (TCO) of a small cell, while providing the additional mobile wireless data offload capacity from Macro Cell to small cell in LTE Heterogeneous Networks (HetNet), to meet such an increase in wireless data demand. The U.S. 5 GHz Unlicensed National Information Infrastructure (U-NII) bands that are currently under consideration for LTE deployment in the unlicensed spectrum contain only a limited number of 20 MHZ channels. Thus in a dense multi-operator deployment scenario, one or more LTE-U small cells have to co-exist and share the same 20 MHz unlicensed channel with each other and with the incumbent Wi-Fi. This dissertation presents a proactive small cell interference mitigation strategy for improving the spectral efficiency of LTE networks in the unlicensed spectrum. It describes the scenario and demonstrate via simulation results, that in the absence of an explicit interference mitigation mechanism, there will be a significant degradation in the overall LTE-U system performance for LTE-U co-channel co-existence in countries such as U.S. that do not mandate Listen-Before-Talk (LBT) regulations. An unlicensed spectrum Inter Cell Interference Coordination (usICIC) mechanism is then presented as a time-domain multiplexing technique for interference mitigation for the sharing of an unlicensed channel by multi-operator LTE-U small cells. Through extensive simulation results, it is demonstrated that the proposed usICIC mechanism will result in 40% or more improvement in the overall LTE-U system performance (throughput) leading to increased wireless communication system capacity. The ever increasing demand for mobile wireless data is also resulting in a dramatic expansion of wireless network infrastructure by all service providers resulting in significant escalation in energy consumption by the wireless networks. This not only has an impact on the recurring operational expanse (OPEX) for the service providers, but importantly the resulting increase in greenhouse gas emission is not good for the environment. Energy efficiency has thus become one of the critical tenets in the design and deployment of Green wireless communication systems. Consequently the market trend for next-generation communication systems has been towards miniaturization to meet this stunning ever increasing demand for mobile wireless data, leading towards the need for scalable distributed and parallel processing system architecture that is energy efficient, and high capacity. Reducing cost and size while increasing capacity, ensuring scalability, and achieving energy efficiency requires several design paradigm shifts. This dissertation presents the design for a next generation wireless communication system that employs new energy efficient distributed and parallel processing system architecture to achieve these goals while leveraging the unlicensed spectrum to significantly increase (by a factor of two) the capacity of the wireless communication system. This design not only significantly reduces the upfront CAPEX, but also the recurring OPEX for the service providers to maintain their next generation wireless communication networks

Parametric, Optimization-Based Study on the Feasibility of a Multisegment Antisolvent Crystallizer for in Situ Fines Removal and Matching of Target Size Distribution

Peer reviewedPostprin

The impact of regulatory changes on the providers of treatment for opioid dependence

In 2000, changes in federal law allowed physicians to receive waivers to use narcotic medications, such as buprenorphine, for treatment of opioid dependence. As of 2006, physicians have been allowed to treat up to 100 patients after spending one year at a 30-patient limit. Physicians may choose to discontinue use of buprenorphine after the patient has successfully discontinued use of the substance of abuse ( withdrawal ), or physicians can keep patients on buprenorphine indefinitely ( maintenance ). The model in this dissertation assumes that demand for treatment of opioid dependence is exogenous but that demand for maintenance treatment can be induced by the physician. Using data from quarterly surveys of physicians from 2006 to 2010, this dissertation analyzes the impact of the higher caseload limit on the number of patients and the treatment path chosen by the physician. It finds support for the conclusion that physicians treat more patients after an increase in the caseload limit. The impact is particularly strong for maintenance, suggesting that the caseload limit discourages maintenance treatment. The dissertation also finds that this effect is stronger for physicians in primary-care type specialties

Non-ergodic phenomena in many-body quantum systems

The assumption of ergodicity is the cornerstone of conventional thermodynamics, connecting the equilibrium properties of macroscopic systems to the chaotic nature of the underlying microscopic dynamics, which eventuates in thermalization and the scrambling of information contained in any generic initial condition. The modern understanding of ergodicity in a quantum mechanical framework is encapsulated in the so-called eigenstate thermalization hypothesis, which asserts that thermalization of an isolated quantum system is a manifestation of the random-like character of individual eigenstates in the bulk of the spectrum of the system's Hamiltonian. In this work, we consider two major exceptions to the rule of generic thermalization in interacting many-body quantum systems: many-body localization, and quantum spin glasses. In the first part, we debate the possibility of localization in a system endowed with a non-Abelian symmetry. We show that, in line with proposed theoretical arguments, such a system is probably delocalized in the thermodynamic limit, but the ergodization length scale is anomalously large, explaining the non-ergodic behavior observed in previous experimental and numerical works. A crucial feature of this system is the quasi-tensor-network nature of its eigenstates, which is dictated by the presence of nontrivial symmetry multiplets. As a consequence, ergodicity may only be restored by extensively large cascades of resonating spins, explaining the system's resistance to delocalization. In the second part, we study the effects of non-ergodic behavior in glassy systems in relation to the possibility of speeding up classical algorithms via quantum resources, namely tunneling across tall free energy barriers. First, we define a pseudo-tunneling event in classical diffusion Monte Carlo (DMC) and characterize the corresponding tunneling rate. Our findings suggest that DMC is very efficient at tunneling in stoquastic problems even in the presence of frustrated couplings, asymptotically outperforming incoherent quantum tunneling. We also analyze in detail the impact of importance sampling, finding that it does not alter the scaling. Next, we study the so-called population transfer (PT) algorithm applied to the problem of energy matching in combinatorial problems. After summarizing some known results on a simpler model, we take the quantum random energy model as a testbed for a thorough, model-agnostic numerical characterization of the algorithm, including parameter setting and quality assessment. From the accessible system sizes, we observe no meaningful asymptotic speedup, but argue in favor of a better performance in more realistic energy landscapes