482 research outputs found
Strategic Proportionality: Limitations on the Use of Force in Modern Armed Conflicts
The nature of modern armed conflicts, combined with traditional interpretations of proportionality, poses serious challenges to the jus ad bellum goal of limiting and controlling wars. In between the jus ad bellum focus on decisions to use force, and the international humanitarian law (IHL) regulation of specific attacks, there is a far-reaching space in which the regulatory role of international law is bereft of much needed clarity. Perhaps the most striking example is in relation to overall casualties of war. If the jus ad bellum is understood as applying to the opening moments of the conflict, then it cannot provide a solution to growing numbers of casualties later in the conflict. Moreover, if it does not apply to non-international armed conflicts, then it is of little use in relation to alleviating the suffering of war for a vast proportion of conflicts in the past half a century and more. IHL is equally unsuited for dealing with overall casualties, as it may be the case that each individual attack is proportionate, but the cumulative number of civilians being killed is slowly rising to intolerable figures. A similar problem arises with regard to assessing other forms of accumulated destruction. This article sets out a new approach to proportionality in armed conflict and the regulation of war. It advocates for a principle of “strategic proportionality,” stemming from general principles of international law and reflected in state practice, and which requires an ongoing assessment throughout the conflict balancing the overall harm against the strategic objectives. The article traces the historical development and aims of the principle of proportionality in war, sets out the scope and aims of strategic proportionality, and provides an analysis of how such a principle can be operationalized in practice
Terminating a common envelope jets supernova impostor event with a super-Eddington blue supergiant
We conducted one-dimensional stellar evolutionary numerical simulations to
build blue supergiant stellar models with a very low-envelope mass and a
super-Eddington luminosity of 10^7Lo that mimic the last phase of a common
envelope evolution (CEE) where a neutron star (NS) accretes mass from the
envelope and launches jets that power the system. Common envelope jets
supernovae (CEJSNe) are CEE transient events where a NS spirals-in inside the
envelope and then the core of a red supergiant (RSG) star accretes mass and
launches jets that power the transient event. In case that the NS (or black
hole) does not enter the core of the RSG the event is a CEJSN-impostor. We
propose that in some cases a CEJSN-impostor event might end with such a phase
of a blue supergiant lasting for several years to few tens of years. The radius
of the blue supergiant is about tens to few hundreds solar radii. We use a
simple prescription to deposit the jets energy into the envelope. We find that
the expected accretion rate of envelope mass onto the NS at the end of the CEE
allows the power of the jets to be as we assume, 10^7Lo. Such a low-mass
envelope might be the end of the RSG envelope, or might be a rebuilt envelope
from mass fallback. Our study of a blue supergiant at the termination of a
CEJSN-impostor event adds to the rich variety of transients that CEJSNe and
CEJSN-impostors might form.Comment: Accepted for publication in MNRA
The depletion of the red supergiant envelope radiative zone during common envelope evolution
We conduct one-dimensional stellar evolution simulations of red supergiant
(RSG) stars that mimic common envelope evolution (CEE) and find that the inner
boundary of the envelope convective zone moves into the initial envelope
radiative zone. The envelope convection practically disappears only when the
RSG radius decreases by about an order of magnitude or more. The implication is
that one cannot split the CEE into one stage during which the companion
spirals-in inside the envelope convective zone and removes it, and a second
slower phase when the companion orbits the initial envelope radiative zone and
a stable mass transfer takes place. At best, this might take place when the
orbital separation is about several solar radii. However, by that time other
processes become important. We conclude that as of yet, the commonly used
alpha-formalism that is based on energy considerations is the best
phenomenological formalism.Comment: Research in Astronomy and Astrophysics, in pres
On the Ability of Graph Neural Networks to Model Interactions Between Vertices
Graph neural networks (GNNs) are widely used for modeling complex
interactions between entities represented as vertices of a graph. Despite
recent efforts to theoretically analyze the expressive power of GNNs, a formal
characterization of their ability to model interactions is lacking. The current
paper aims to address this gap. Formalizing strength of interactions through an
established measure known as separation rank, we quantify the ability of
certain GNNs to model interaction between a given subset of vertices and its
complement, i.e. between sides of a given partition of input vertices. Our
results reveal that the ability to model interaction is primarily determined by
the partition's walk index -- a graph-theoretical characteristic that we define
by the number of walks originating from the boundary of the partition.
Experiments with common GNN architectures corroborate this finding. As a
practical application of our theory, we design an edge sparsification algorithm
named Walk Index Sparsification (WIS), which preserves the ability of a GNN to
model interactions when input edges are removed. WIS is simple, computationally
efficient, and markedly outperforms alternative methods in terms of induced
prediction accuracy. More broadly, it showcases the potential of improving GNNs
by theoretically analyzing the interactions they can model
Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networks
In the pursuit of explaining implicit regularization in deep learning,
prominent focus was given to matrix and tensor factorizations, which correspond
to simplified neural networks. It was shown that these models exhibit an
implicit tendency towards low matrix and tensor ranks, respectively. Drawing
closer to practical deep learning, the current paper theoretically analyzes the
implicit regularization in hierarchical tensor factorization, a model
equivalent to certain deep convolutional neural networks. Through a dynamical
systems lens, we overcome challenges associated with hierarchy, and establish
implicit regularization towards low hierarchical tensor rank. This translates
to an implicit regularization towards locality for the associated convolutional
networks. Inspired by our theory, we design explicit regularization
discouraging locality, and demonstrate its ability to improve the performance
of modern convolutional networks on non-local tasks, in defiance of
conventional wisdom by which architectural changes are needed. Our work
highlights the potential of enhancing neural networks via theoretical analysis
of their implicit regularization.Comment: Accepted to ICML 202
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