Enforcing efficient equilibria in network design games via subsidies

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.Comment: 30 pages, 7 figure

Approximate Pure Nash Equilibria in Weighted Congestion Games: Existence, Efficient Computation, and Structure

We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential function arguments. Unfortunately, this proof of existence is inefficient and computing equilibria is such games is a {\sf PLS}-hard problem. The situation gets worse when superlinear latency functions come into play; in this case, the Nash dynamics of the game may contain cycles and equilibria may not even exist. Given these obstacles, we consider approximate equilibria as alternative solution concepts. Do such equilibria exist? And if so, can we compute them efficiently? We provide positive answers to both questions for weighted congestion games with polynomial latency functions by exploiting an "approximation" of such games by a new class of potential games that we call $\Psi$-games. This allows us to show that these games have $d!$-approximate equilibria, where $d$ is the maximum degree of the latency functions. Our main technical contribution is an efficient algorithm for computing O(1)-approximate equilibria when $d$ is a constant. For games with linear latency functions, the approximation guarantee is $\frac{3+\sqrt{5}}{2}+O(\gamma)$ for arbitrarily small $\gamma>0$; for latency functions with maximum degree $d\geq 2$, it is $d^{2d+o(d)}$. The running time is polynomial in the number of bits in the representation of the game and $1/\gamma$. As a byproduct of our techniques, we also show the following structural statement for weighted congestion games with polynomial latency functions of maximum degree $d\geq 2$: polynomially-long sequences of best-response moves from any initial state to a $d^{O(d^2)}$-approximate equilibrium exist and can be efficiently identified in such games as long as $d$ is constant.Comment: 31 page

Efficient computation of approximate pure Nash equilibria in congestion games

Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {\sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes O(1)-approximate Nash equilibria in these games. In particular, for congestion games with linear latency functions, our algorithm computes $(2+\epsilon)$-approximate pure Nash equilibria in time polynomial in the number of players, the number of resources and $1/\epsilon$. It also applies to games with polynomial latency functions with constant maximum degree $d$; there, the approximation guarantee is $d^{O(d)}$. The algorithm essentially identifies a polynomially long sequence of best-response moves that lead to an approximate equilibrium; the existence of such short sequences is interesting in itself. These are the first positive algorithmic results for approximate equilibria in non-symmetric congestion games. We strengthen them further by proving that, for congestion games that deviate from our mild assumptions, computing $\rho$-approximate equilibria is {\sf PLS}-complete for any polynomial-time computable $\rho$

Ride Sharing with a Vehicle of Unlimited Capacity

A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle travels through the graph, carrying each object from its origin to its destination without any bound on the number of objects that can be simultaneously transported. The vehicle starts and terminates its ride at given nodes, and the goal is to compute a minimum-cost ride satisfying all requests. This ride sharing problem is shown to be tractable on paths by designing a O(h*log(h)+n) algorithm, with h being the number of distinct requests and with n being the number of nodes in the path. The algorithm is then used as a subroutine to efficiently solve instances defined over cycles, hence covering all graphs with maximum degree 2. This traces the frontier of tractability, since NP-hard instances are exhibited over trees whose maximum degree is 3

Structural communication between the GTPase Sec4p and its activator Sec2p: Determinants of GEF activity and early deformations to nucleotide release

Ras GTPases are molecular switches that cycle between OFF and ON states depending on the bound nucleotide (i.e. GDP-bound and GTP-bound, respectively).The Rab GTPase, Sec4p, plays regulatory roles in multiple steps of intracellular vesicle trafficking. Nucleotide release is catalyzed by the Guanine Nucleotide Exchange Factor (GEF) Sec2p.Here, the integration of structural information with molecular dynamics (MD) simulations addressed a number of questions concerning the intrinsic and stimulated dynamics of Sec2p and Sec4p as well as the chain of structural deformations leading to GEF-assisted activation of the Rab GTPase.Sec2p holds an intrinsic ability to adopt the conformation found in the crystallographic complexes with Sec4p, thus suggesting that the latter selects and shifts the conformational equilibrium towards a pre-existing bound-like conformation of Sec2p.The anchoring of Sec4p to a suitable conformation of Sec2p favors the Sec2p-assisted pulling on itself of the a1/switch 1 (SWI) loop and of SWI, which loose any contact with GDP. Those deformations of Sec4p would occur earlier. Formation of the final Sec2p-Sec4p hydrophobic interface, accomplishes later. Disruption of the nucleotide cage would cause firstly loss of interactions with the guanine ring and sec-ondly loss of interactions with the phosphates.The ease in sampling the energy landscape and adopting a bound-like conformation likely favors the catalyzing ability of GEFs for Ras GTPases.(c) 2022 Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Bio-technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/)

Network and atomistic simulations unveil the structural determinants of mutations linked to retinal diseases

A number of incurable retinal diseases causing vision impairments derive from alterations in visual phototransduction. Unraveling the structural determinants of even monogenic retinal diseases would require network-centered approaches combined with atomistic simulations. The transducin G38D mutant associated with the Nougaret Congenital Night Blindness (NCNB) was thoroughly investigated by both mathematical modeling of visual phototransduction and atomistic simulations on the major targets of the mutational effect. Mathematical modeling, in line with electrophysiological recordings, indicates reduction of phosphodiesterase 6 (PDE) recognition and activation as the main determinants of the pathological phenotype. Sub-microsecond molecular dynamics (MD) simulations coupled with Functional Mode Analysis improve the resolution of information, showing that such impairment is likely due to disruption of the PDEgamma binding cavity in transducin. Protein Structure Network analyses additionally suggest that the observed slight reduction of theRGS9-catalyzed GTPase activity of transducin depends on perturbed communication between RGS9 and GTP binding site. These findings provide insights into the structural fundamentals of abnormal functioning of visual phototransduction caused by a missense mutation in one component of the signaling network. This combination of network-centered modeling with atomistic simulations represents a paradigm for future studies aimed at thoroughly deciphering the structural determinants of genetic retinal diseases. Analogous approaches are suitable to unveil the mechanism of information transfer in any signaling network either in physiological or pathological conditions

A Small Chaperone Improves Folding and Routing of Rhodopsin Mutants Linked to Inherited Blindness

The autosomal dominant form of retinitis pigmentosa (adRP) is a blindness-causing conformational disease largely linked to mutations of rhodopsin. Molecular simulations coupled to the graph-based protein structure network (PSN) analysis and in vitro experiments were conducted to determine the effects of 33 adRP rhodopsin mutations on the structure and routing of the opsin protein. The integration of atomic and subcellular levels of analysis was accomplished by the linear correlation between indices of mutational impairment in structure network and in routing. The graph-based index of structural perturbation served also to divide the mutants in four clusters, consistent with their differences in subcellular localization and responses to 9-cis retinal. The stability core of opsin inferred from PSN analysis was targeted by virtual screening of over 300,000 anionic compounds leading to the discovery of a reversible orthosteric inhibitor of retinal binding more effective than retinal in improving routing of three adRP mutants

Generation of induced pluripotent stem cell line CSSi008-A (4698) from a patient affected by advanced stage of Dentato-Rubral-Pallidoluysian atrophy (DRPLA)

Abstract Dentato-Rubral-pallidoluysian atrophy (DRPLA) is a rare autosomal, dominant, progressive neurodegenerative disease that causes involuntary movements, mental and emotional problems. DRPLA is caused by a mutation in the ATN1 gene that encodes for an abnormal polyglutamine stretch in the atrophin-1 protein. DRPLA is most common in the Japanese population, where it has an estimated incidence of 2 to 7 per million people. This condition has also been seen in families from North America and Europe. We obtained a reprogrammed iPSC line from a Caucasian patient with a juvenile onset of the disease, carrying 64 CAG repeat expansion in the ATN1 gene