96 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Improved algorithms for finding fixed-degree isogenies between supersingular elliptic curves
Finding isogenies between supersingular elliptic curves is a natural algorithmic problem which is known to be equivalent to computing the curves\u27 endomorphism rings.
When the isogeny is additionally required to have a specific degree , the problem appears to be somewhat different in nature, yet it is also considered a hard problem in isogeny-based cryptography.
Let be supersingular elliptic curves over . We present improved classical and quantum algorithms that compute an isogeny of degree between and if it exists. Let the sought-after degree be for some .
Our essentially memory-free algorithms have better time complexity than meet-in-the-middle algorithms, which require exponential memory storage, in the range on a classical computer and quantum improvements in the range
Safe navigation and human-robot interaction in assistant robotic applications
L'abstract Ăš presente nell'allegato / the abstract is in the attachmen
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Streaming algorithms for evaluating noisy judges on unlabeled data -- binary classification
The evaluation of noisy binary classifiers on unlabeled data is treated as a
streaming task: given a data sketch of the decisions by an ensemble, estimate
the true prevalence of the labels as well as each classifier's accuracy on
them. Two fully algebraic evaluators are constructed to do this. Both are based
on the assumption that the classifiers make independent errors. The first is
based on majority voting. The second, the main contribution of the paper, is
guaranteed to be correct. But how do we know the classifiers are independent on
any given test? This principal/agent monitoring paradox is ameliorated by
exploiting the failures of the independent evaluator to return sensible
estimates. A search for nearly error independent trios is empirically carried
out on the \texttt{adult}, \texttt{mushroom}, and \texttt{two-norm} datasets by
using the algebraic failure modes to reject evaluation ensembles as too
correlated. The searches are refined by constructing a surface in evaluation
space that contains the true value point. The algebra of arbitrarily correlated
classifiers permits the selection of a polynomial subset free of any
correlation variables. Candidate evaluation ensembles are rejected if their
data sketches produce independent estimates too far from the constructed
surface. The results produced by the surviving ensembles can sometimes be as
good as 1\%. But handling even small amounts of correlation remains a
challenge. A Taylor expansion of the estimates produced when independence is
assumed but the classifiers are, in fact, slightly correlated helps clarify how
the independent evaluator has algebraic `blind spots'.Comment: 23 pages, 5 figure
A Direttissimo Algorithm for Equidimensional Decomposition
We describe a recursive algorithm that decomposes an algebraic set into
locally closed equidimensional sets, i.e. sets which each have irreducible
components of the same dimension. At the core of this algorithm, we combine
ideas from the theory of triangular sets, a.k.a. regular chains, with Gr\"obner
bases to encode and work with locally closed algebraic sets. Equipped with
this, our algorithm avoids projections of the algebraic sets that are
decomposed and certain genericity assumptions frequently made when decomposing
polynomial systems, such as assumptions about Noether position. This makes it
produce fine decompositions on more structured systems where ensuring
genericity assumptions often destroys the structure of the system at hand.
Practical experiments demonstrate its efficiency compared to state-of-the-art
implementations
Semidefinite programming relaxations for quantum correlations
Semidefinite programs are convex optimisation problems involving a linear
objective function and a domain of positive semidefinite matrices. Over the
last two decades, they have become an indispensable tool in quantum information
science. Many otherwise intractable fundamental and applied problems can be
successfully approached by means of relaxation to a semidefinite program. Here,
we review such methodology in the context of quantum correlations. We discuss
how the core idea of semidefinite relaxations can be adapted for a variety of
research topics in quantum correlations, including nonlocality, quantum
communication, quantum networks, entanglement, and quantum cryptography.Comment: To be submitted to Reviews of Modern Physic
Expanding the Horizons of Manufacturing: Towards Wide Integration, Smart Systems and Tools
This research topic aims at enterprise-wide modeling and optimization (EWMO) through the development and application of integrated modeling, simulation and optimization methodologies, and computer-aided tools for reliable and sustainable improvement opportunities within the entire manufacturing network (raw materials, production plants, distribution, retailers, and customers) and its components. This integrated approach incorporates information from the local primary control and supervisory modules into the scheduling/planning formulation. That makes it possible to dynamically react to incidents that occur in the network components at the appropriate decision-making level, requiring fewer resources, emitting less waste, and allowing for better responsiveness in changing market requirements and operational variations, reducing cost, waste, energy consumption and environmental impact, and increasing the benefits. More recently, the exploitation of new technology integration, such as through semantic models in formal knowledge models, allows for the capture and utilization of domain knowledge, human knowledge, and expert knowledge toward comprehensive intelligent management. Otherwise, the development of advanced technologies and tools, such as cyber-physical systems, the Internet of Things, the Industrial Internet of Things, Artificial Intelligence, Big Data, Cloud Computing, Blockchain, etc., have captured the attention of manufacturing enterprises toward intelligent manufacturing systems
Mathematical models of cell signalling in heterogeneous populations
Immune cells express thousands of receptors on their membrane surface to sense their environment and communicate with each other. Receptors bind specifically to extra-cellular molecules called ligands. The binding of a ligand to its receptor initiates an intra-cellular signalling cascade which leads to the control of cellular fate, such as division, death, migration or differentiation. As every cell expresses a different number of receptors, each cell responds differently to a given ligand. First motivated by seemingly paradoxical experimental observations on the interleukin-7/interleukin-7 receptor (IL-7/IL-7R) receptor-ligand system, this thesis investigates how receptor copy numbers impact the cell's response, as measured by the amplitude and the half-maximal effective concentration (or EC50). In particular, deterministic mathematical models of various receptor-ligand systems are developed. For each model, making use of algebraic tools, such as Grobner bases, analytic expressions for the amplitude and the EC50 are computed. Such expressions allow one to identify precisely how a cell's response depends on the receptor core structure, namely receptor chain copy numbers and receptor architecture. They also reduce numerical errors and facilitate parameter inference, as demonstrated by the fitting of two IL-7R models to the motivating experimental data set.
The results obtained are generalised to a larger family of receptor-ligand systems, for which the amplitude is computed without the use of advanced algebraic tools.
Finally, as the immune system relies on the coordination of many cells to fight pathogens, the complex relationship between the cell population dynamics and the receptor copy number distribution in the cellular population is examined. To this end, agent-based models of increasing complexity, which model the competition for interleukin-2 (IL-2) within the T cell population, are constructed, by adding stochastic cellular events one at a time. A mathematical description of each model is provided, which enables us, when possible, to derive the desired receptor copy number distribution (in this case for the IL-2 receptor)
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