Smoothed Efficient Algorithms and Reductions for Network Coordination Games

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case. This is a potential game where the sequential-better-response algorithm is known to converge to a pure NE, albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial) smoothed complexity when the underlying game graph is a complete (resp. arbitrary) graph, and every player has constantly many strategies. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in most known smoothed analysis results. Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from $2$-strategy network coordination games to local-max-cut, and from $k$-strategy games (with arbitrary $k$) to local-max-cut up to two flips. The former together with the recent result of [BCC18] gives an alternate $O(n^8)$-time smoothed algorithm for the $2$-strategy case. This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another. For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful definition of the matrix which captures the increase in potential, a tighter union bound on adversarial sequences, and balancing it with good enough rank bounds. We believe that the approach and notions developed herein could be of interest in addressing the smoothed complexity of other potential and/or congestion games

Dynamic Data-Race Detection Through the Fine-Grained Lens

Data races are among the most common bugs in concurrency. The standard approach to data-race detection is via dynamic analyses, which work over executions of concurrent programs, instead of the program source code. The rich literature on the topic has created various notions of dynamic data races, which are known to be detected efficiently when certain parameters (e.g., number of threads) are small. However, the fine-grained complexity of all these notions of races has remained elusive, making it impossible to characterize their trade-offs between precision and efficiency. In this work we establish several fine-grained separations between many popular notions of dynamic data races. The input is an execution trace ? with ? events, ? threads and ? locks. Our main results are as follows. First, we show that happens-before HB races can be detected in O(?? min(?, ?)) time, improving over the standard O(?? ?) bound when ? = o(?). Moreover, we show that even reporting an HB race that involves a read access is hard for 2-orthogonal vectors (2-OV). This is the first rigorous proof of the conjectured quadratic lower-bound in detecting HB races. Second, we show that the recently introduced synchronization-preserving races are hard to detect for 3-OV and thus have a cubic lower bound, when ? = ?(?). This establishes a complexity separation from HB races which are known to be strictly less expressive. Third, we show that lock-cover races are hard for 2-OV, and thus have a quadratic lower-bound, even when ? = 2 and ? = ?(log ?). The similar notion of lock-set races is known to be detectable in O(?? ?) time, and thus we achieve a complexity separation between the two. Moreover, we show that lock-set races become hitting-set (HS)-hard when ? = ?(?), and thus also have a quadratic lower bound, when the input is sufficiently complex. To our knowledge, this is the first work that characterizes the complexity of well-established dynamic race-detection techniques, allowing for a rigorous comparison between them

Biologically inspired design of feedback control systems implemented using DNA strand displacement reactions

The use of abstract chemical reaction networks (CRNs) as a modelling and design framework for the implementation of computing and control circuits using enzyme-free, entropy driven DNA strand displacement (DSD) reactions is starting to garner widespread attention in the area of synthetic biology. Previous work in this area has demonstrated the theoretical plausibility of using this approach to design biomolecular feedback control systems based on classical proportional-integral (PI) controllers, which may be constructed from CRNs implementing gain, summation and integrator operators. Here, we propose an alternative design approach that utilises the abstract chemical reactions involved in cellular signalling cycles to implement a biomolecular controller - termed a signalling-cycle (SC) controller. We compare the performance of the PI and SC controllers in closed-loop with a nonlinear second-order chemical process. Our results show that the SC controller outperforms the PI controller in terms of both performance and robustness, and also requires fewer abstract chemical reactions to implement, highlighting its potential usefulness in the construction of biomolecular control circuits

Implementing nonlinear feedback controllers using DNA strand displacement reactions

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs

Biomolecular implementation of nonlinear system theoretic operators

Synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications, including biomass maximization, nanoscale drug delivery, and many others. In this paper, we present new results on how abstract chemical reactions can be used to implement commonly used system theoretic operators such as the polynomial functions, rational functions and Hill-type nonlinearity. We first describe how idealised versions of multi-molecular reactions, catalysis, annihilation, and degradation can be combined to implement these operators. We then show how such chemical reactions can be implemented using enzyme-free, entropy-driven DNA reactions. Our results are illustrated through three applications: (1) implementation of a Stan-Sepulchre oscillator, (2) the computation of the ratio of two signals, and (3) a PI+antiwindup controller for regulating the output of a static nonlinear plant

Chondroprotective Potential of Fruit Extracts of Phyllanthus emblica in Osteoarthritis

There is a need for effective nutraceuticals for osteoarthritis care. The fruit of Phyllanthus emblica is used as a powerful rejuvenator in Ayurvedic medicine. This study measured the chondroprotective potential of P. emblica (‘Amalaki’) fruits in vitro. We used aqueous extracts of unprocessed P. emblica fruit powder (powder A), and the powder obtained after hot water extraction and drying of powder A (powder B). Chondroprotection was measured in three different assay systems. First, we tested the effects of both fruit powders on the activities of the enzymes hyaluronidase and collagenase type 2. Second, an in vitro model of cartilage degradation was set-up with explant cultures of articular knee cartilage from osteoarthritis patients. Cartilage damage was assayed by measuring glycosaminoglycan release from explants treated with/without P. emblica fruit powders. Aqueous extracts of both fruit powders significantly inhibited the activities of hyaluronidase and collagenase type 2 in vitro. Third, in the explant model of cartilage matrix damage, extracts of glucosamine sulphate and powder B (0.05 mg/ml) exhibited statistically significant, long-term chondroprotective activity in cartilage explants from 50% of the patients tested. This result is important since glucosamine sulphate is the leading nutraceutical for osteoarthritis. Powder A induced a statistically significant, short-term chondroprotective activity in cartilage explants from all of the patients tested. This is the first study to identify and quantitate new chondroprotective activities of P. emblica fruits. These data provide pilot pre-clinical evidence for the use of P. emblica fruits as a chondroprotective agent in osteoarthritis therapy

Evolution of a physiological pH 6.8 bicarbonate buffer system: application to the dissolution testing of enteric coated products.

The use of compendial pH 6.8 phosphate buffer to assess dissolution of enteric coated products gives rise to poor in vitro-in vivo correlations because of the inadequacy of the buffer to resemble small intestinal fluids. A more representative and physiological medium, pH 6.8 bicarbonate buffer, was developed to evaluate the dissolution behaviour of enteric coatings. The bicarbonate system was evolved from pH7.4 Hanks balanced salt solution to produce a pH 6.8 bicarbonate buffer (modified Hanks buffer, mHanks), which resembles the ionic composition and buffer capacity of intestinal milieu. Prednisolone tablets were coated with a range of enteric polymers: hypromellose phthalate (HP-50 and HP-55), cellulose acetate phthalate (CAP), hypromellose acetate succinate (HPMCAS-LF and HPMCAS-MF), methacrylic acid copolymers (EUDRAGIT® L100-55, EUDRAGIT® L30D-55 and EUDRAGIT® L100) and polyvinyl acetate phthalate (PVAP). Dissolution of coated tablets was carried out using USP-II apparatus in 0.1M HCl for 2h followed by pH 6.8 phosphate buffer or pH 6.8 mHanks bicarbonate buffer. In pH 6.8 phosphate buffer, the various enteric polymer coated products displayed rapid and comparable dissolution profiles. In pH 6.8 mHanks buffer, drug release was delayed and marked differences were observed between the various coated tablets, which is comparable to the delayed disintegration times reported in the literature for enteric coated products in the human small intestine. In summary, the use of pH 6.8 physiological bicarbonate buffer (mHanks) provides more realistic and discriminative in vitro release assessment of enteric coated formulations compared to compendial phosphate buffer