4,168 research outputs found
Complex-linear invariants of biochemical networks
The nonlinearities found in molecular networks usually prevent mathematical
analysis of network behaviour, which has largely been studied by numerical
simulation. This can lead to difficult problems of parameter determination.
However, molecular networks give rise, through mass-action kinetics, to
polynomial dynamical systems, whose steady states are zeros of a set of
polynomial equations. These equations may be analysed by algebraic methods, in
which parameters are treated as symbolic expressions whose numerical values do
not have to be known in advance. For instance, an "invariant" of a network is a
polynomial expression on selected state variables that vanishes in any steady
state. Invariants have been found that encode key network properties and that
discriminate between different network structures. Although invariants may be
calculated by computational algebraic methods, such as Gr\"obner bases, these
become computationally infeasible for biologically realistic networks. Here, we
exploit Chemical Reaction Network Theory (CRNT) to develop an efficient
procedure for calculating invariants that are linear combinations of
"complexes", or the monomials coming from mass action. We show how this
procedure can be used in proving earlier results of Horn and Jackson and of
Shinar and Feinberg for networks of deficiency at most one. We then apply our
method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity
regulator and the mammalian
6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator,
whose networks have deficiencies up to four. We show that bifunctionality leads
to different forms of concentration control that are robust to changes in
initial conditions or total amounts. Finally, we outline a systematic procedure
for using complex-linear invariants to analyse molecular networks of any
deficiency.Comment: 36 pages, 6 figure
Edge Intersection Graphs of L-Shaped Paths in Grids
In this paper we continue the study of the edge intersection graphs of one
(or zero) bend paths on a rectangular grid. That is, the edge intersection
graphs where each vertex is represented by one of the following shapes:
,, , , and we consider zero bend
paths (i.e., | and ) to be degenerate s. These graphs, called
-EPG graphs, were first introduced by Golumbic et al (2009). We consider
the natural subclasses of -EPG formed by the subsets of the four single
bend shapes (i.e., {}, {,},
{,}, and {,,}) and we
denote the classes by [], [,],
[,], and [,,]
respectively. Note: all other subsets are isomorphic to these up to 90 degree
rotation. We show that testing for membership in each of these classes is
NP-complete and observe the expected strict inclusions and incomparability
(i.e., [] [,],
[,] [,,]
-EPG; also, [,] is incomparable with
[,]). Additionally, we give characterizations and
polytime recognition algorithms for special subclasses of Split
[].Comment: 14 pages, to appear in DAM special issue for LAGOS'1
Finite automata with advice tapes
We define a model of advised computation by finite automata where the advice
is provided on a separate tape. We consider several variants of the model where
the advice is deterministic or randomized, the input tape head is allowed
real-time, one-way, or two-way access, and the automaton is classical or
quantum. We prove several separation results among these variants, demonstrate
an infinite hierarchy of language classes recognized by automata with
increasing advice lengths, and establish the relationships between this and the
previously studied ways of providing advice to finite automata.Comment: Corrected typo
Phosphorus-Containing Food Additives in the Food Supply-An Audit of Products on Supermarket Shelves
Objectives: Phosphorus (P)-containing food additives pose a risk for chronic kidney disease (CKD) patients. We aimed to investigate the prevalence of P-containing additives in the Finnish food supply across different food categories to evaluate their burden in CKD, reflecting the situation in Europe. Methods: The dataset of 6,176 products was obtained in June-August 2019 from the foodie.fi website, which contains all foodstuffs sold in the grocery stores of the S Group (46% of the Finnish market share in 2019). The food category, full product name, type of P additive (inorganic, organic, and natural P-containing), and reporting methods (name or E number) of P additives were recorded. Duplicates and products lacking ingredient information were excluded. Results: The prevalence of P additives was 36% in the final sample (n 5 5,149). Among food categories, the prevalence varied from 4% in dairy-based snacks to 67% in meat products. Altogether 17 different P additives were observed. Inorganic P additives were the most common P additive type, present in 20% of foodstuffs. Natural P-containing additives were observed in 19% and organic P additives in 2% of foodstuffs. The most commonly used P additives were lecithin (E 322), pyrophosphate (E 450), and triphosphate (E 451). E number was used as a reporting method in 49% of foodstuffs, and full name in 44% of foodstuffs. Reporting by E number was particularly common in the products containing inorganic P. Conclusions: The use of P additives is common in the Finnish food supply, indicating the situation in Europe. The high prevalence of inorganic, that is, the most absorbable and potentially most harmful P additives in particular food groups, and their usual reporting only by E numbers can create challenges in CKD dietary counseling. (c) 2021 The Authors. Published by Elsevier Inc. on behalf of the National Kidney Foundation, Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe
Dynamic Range Majority Data Structures
Given a set of coloured points on the real line, we study the problem of
answering range -majority (or "heavy hitter") queries on . More
specifically, for a query range , we want to return each colour that is
assigned to more than an -fraction of the points contained in . We
present a new data structure for answering range -majority queries on a
dynamic set of points, where . Our data structure uses O(n)
space, supports queries in time, and updates in amortized time. If the coordinates of the points are integers,
then the query time can be improved to . For constant values of , this improved query
time matches an existing lower bound, for any data structure with
polylogarithmic update time. We also generalize our data structure to handle
sets of points in d-dimensions, for , as well as dynamic arrays, in
which each entry is a colour.Comment: 16 pages, Preliminary version appeared in ISAAC 201
Percolation of satisfiability in finite dimensions
The satisfiability and optimization of finite-dimensional Boolean formulas
are studied using percolation theory, rare region arguments, and boundary
effects. In contrast with mean-field results, there is no satisfiability
transition, though there is a logical connectivity transition. In part of the
disconnected phase, rare regions lead to a divergent running time for
optimization algorithms. The thermodynamic ground state for the NP-hard
two-dimensional maximum-satisfiability problem is typically unique. These
results have implications for the computational study of disordered materials.Comment: 4 pages, 4 fig
Convex Independence in Permutation Graphs
A set C of vertices of a graph is P_3-convex if every vertex outside C has at
most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest
P_3-convex set that contains A. A set M is convexly independent if for every
vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of
vertices that a convexly independent set in a permutation graph can have, can
be computed in polynomial time
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Sparse stretching for solving sparse-dense linear least-squares problems
Large-scale linear least-squares problems arise in a wide range of practical applications. In some cases, the system matrix contains a small number of dense rows. These make the problem significantly harder to solve because their presence limits the direct applicability of sparse matrix techniques. In particular, the normal matrix is (close to) dense,
so that forming it is impractical. One way to help overcome the dense row problem is to employ matrix stretching.
Stretching is a sparse matrix technique that improves sparsity by making the least-squares problem larger.
We show that standard stretching can still result in the normal matrix for the stretched problem having an unacceptably large amount of fill. This motivates us to propose a new sparse stretching strategy that performs the stretching so as to limit the fill in the normal matrix and its Cholesky factor. Numerical examples from real problems
are used to illustrate the potential gains
Routing Games over Time with FIFO policy
We study atomic routing games where every agent travels both along its
decided edges and through time. The agents arriving on an edge are first lined
up in a \emph{first-in-first-out} queue and may wait: an edge is associated
with a capacity, which defines how many agents-per-time-step can pop from the
queue's head and enter the edge, to transit for a fixed delay. We show that the
best-response optimization problem is not approximable, and that deciding the
existence of a Nash equilibrium is complete for the second level of the
polynomial hierarchy. Then, we drop the rationality assumption, introduce a
behavioral concept based on GPS navigation, and study its worst-case efficiency
ratio to coordination.Comment: Submission to WINE-2017 Deadline was August 2nd AoE, 201
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