IST Austria: PubRep (Institute of Science and Technology)
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ISTA Thesis
No full textThis thesis comprises two distinct projects, each offering unique insights into fundamental
cellular processes. While distinct in their focus, these different perspectives have a common
theme: chemiosmotic theory and utilisation of the proton gradient for driving the essential
processes like auxin efflux and ATP synthesis, effectively bridging the membrane protein
structure and function from the realms of plant biology and cellular bioenergetics.
The first project of this thesis centres on the characterisation of PIN proteins, a class of
transmembrane transporters pivotal in the regulation of auxin transport and distribution in
plants. PINs form a conserved and phylogenetically abundant group of transporters present in
land plants and certain algae. Despite their great importance, they were one of the few elusive
proteins essential for plant development not to be structurally and mechanistically
characterised since their discovery almost 30 years ago. This work aimed to uncover the
structural and functional dynamics of the PIN protein-mediated auxin transport using an array
of experimental techniques, including protein purification, biochemical assays and structural
analysis. Through an exhaustive screening process that took several years and included testing
different PIN homologues, expression systems, constructs, and purification conditions, we
developed a robust protocol for isolating the pure, stable, and monodisperse PIN8 protein.
Moreover, utilising biophysical methods and buffer screening, we demonstrated that PIN8
exhibits detergent and pH-dependent stability, with mild detergents and lower pH (5.0 and 6.0)
being optimal for the stability of the protein. Using SEC-MALS and crosslinking, we
determined that PIN8 forms dimers, which was confirmed by our structural studies. We
obtained a cryo-EM map of PIN8 at pH 6.0, and, compared to recently published structures,
our map implies major pH-dependent conformational changes and possibly utilisation of the
proton gradient in the transport mechanism.
The subject of the second project was F1Fo-ATP synthase, an enzyme complex fundamental
to cellular energy metabolism. Through an approach integrating biochemical assays and
structural analysis, this research aimed to unveil the molecular mechanism of inhibition of ATP
synthase by yaku´amide, a bioactive compound with potential therapeutic implications. Using
submitochondrial particles and purified F1Fo-ATP synthase, we demonstrated that, contrary to
published data, yaku´amide inhibits both ATP hydrolysis and ATP synthesis reactions.
Moreover, we found that yaku´amide inhibitory activity is proton motive force (pmf)
dependent, with lower inhibition in a more coupled system. Utilising cryo-EM, we obtained
maps and models for the three main rotational states of murine ATP synthase (State 1 at 3.0 Å,
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State 2 at 3.1 Å, and State 3 at 3.2 Å, overall). We observed several new features in our maps;
however, we cannot definitively determine the exact mechanism of yaku amide’s inhibition on
the protein due to either resolution limits or suboptimal binding of the inhibitor
The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass
No full textWe study the Fröhlich polaron model in R3, and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper bound proved earlier (Mitrouskas et al. in Forum Math. Sigma 11:1–52, 2023), it shows that the energy is approximately parabolic below the continuum threshold, and that the polaron’s effective mass (defined as the semi-latus rectum of the
parabola) is given by the celebrated Landau–Pekar formula. In particular, it diverges as α4 for large coupling constant α
ISTA Thesis
No full textIn the modern age of machine learning, artificial neural networks have become an integral part
of many practical systems. One of the key ingredients of the success of the deep learning
approach is recent computational advances which allowed the training of models with billions
of parameters on large-scale data. Such over-parameterized and data-hungry regimes pose a
challenge for the theoretical analysis of modern models since “classical” statistical wisdom
is no longer applicable. In this view, it is paramount to extend or develop new machinery
that will allow tackling the neural network analysis under new challenging asymptotic regimes,
which is the focus of this thesis.
Large neural network systems are usually optimized via “local” search algorithms, such
as stochastic gradient descent (SGD). However, given the high-dimensional nature of the
parameter space, it is a priori not clear why such a crude “local” approach works so remarkably
well in practice. We take a step towards demystifying this phenomenon by showing that
the landscape of the SGD training dynamics exhibits a few beneficial properties for the
optimization. First, we show that along the SGD trajectory an over-parameterized network
is dropout stable. The emergence of dropout stability allows to conclude that the minima
found by SGD are connected via a continuous path of small loss. This in turn means that
the high-dimensional landscape of the neural network optimization problem is provably not so
unfavourable to gradient-based training, due to mode connectivity. Next, we show that SGD
for an over-parameterized network tends to find solutions that are functionally more “simple”.
This in turn means that the SGD minima are more robust, since a less complicated solution
will less likely overfit the data. More formally, for a prototypical example of a wide two-layer
ReLU network on a 1d regression task we show that the SGD algorithm is implicitly selective in
its choice of an interpolating solution. Namely, at convergence the neural network implements
a piece-wise linear function with the number of linear regions depending only on the amount
of training data. This is in contrast to a “smooth”-like behaviour which one would expect
given such a severe over-parameterization of the model.
Diverging from the generic supervised setting of classification and regression problems, we
analyze an auto-encoder model that is commonly used for representation learning and data
compression. Despite the wide applicability of the auto-encoding paradigm, the theoretical
understanding of their behaviour is limited even in the simplistic shallow case. The related
work is restricted to extreme asymptotic regimes in which the auto-encoder is either severely
over-parameterized or under-parameterized. In contrast, we provide a tight characterization
for the 1-bit compression of Gaussian signals in the challenging proportional regime, i.e., the
input dimension and the size of the compressed representation obey the same asymptotics.
We also show that gradient-based methods are able to find a globally optimal solution and
that the predictions made for Gaussian data extrapolate beyond - to the case of compression
of natural images. Next, we relax the Gaussian assumption and study more structured input
sources. We show that the shallow model is sometimes agnostic to the structure of the data
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which results in a Gaussian-like behaviour. We prove that making the decoding component
slightly less shallow is already enough to escape the “curse” of Gaussian performance
FRESCO: The Paschen-α star-forming sequence at cosmic noon
No full textWe present results from the JWST First Reionization Epoch Spectroscopically Complete Observations survey on the star-forming sequence (SFS) of galaxies at 1.0 9.5 that are lower than found in many earlier studies by up to 0.6 dex, but in good agreement with recent results obtained with the Prospector fitting framework. The difference (log(SFR(Paα)-SFR(Prospector)) is −0.09 ± 0.04 dex at 1010−11M⊙. We also measure the empirical relation between Paschen-α luminosity and rest-frame H-band magnitude and find that the scatter is only 0.04 dex lower than that of the SFR–M* relation and is much lower than the systematic differences among relations in the literature due to various methods of converting observed measurements to physical properties. We additionally identify examples of sources—that, with standard cutoffs via the UVJ diagram, would be deemed quiescent—with significant (log(sSFR)> −11 yr−1), typically extended, Paschen-α emission. Our results may be indicative of the potential unification of methods used to derive the SFS with careful selection of star-forming galaxies and independent SFR and stellar mass indicators
LIPIcs
No full textWe study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model iff every deterministic refinement of is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between and ℬ: every strategy that resolves the nondeterminism of is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata
The average number of integral points on the congruent number curves
No full textWe show that the total number of non-torsion integral points on the elliptic curves ED : y
2 = x3 − D2x, where D ranges over positive squarefree integers less than N, is O(N(log N)
−1/4+ǫ). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown’s method on estimating the average size of the 2-Selmer group of the curves in this family
LIPIcs
No full textIn our companion paper "Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds" we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape (either manifold or general set with positive reach) such that one can infer the homotopy of from the union of balls with some radius centred at P, both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting
Developmental transformation of Ca2+ channel-vesicle nanotopography at a central GABAergic synapse
No full textThe coupling between Ca2+ channels and release sensors is a key factor defining the signaling properties of a synapse. However, the coupling nanotopography at many synapses remains unknown, and it is unclear how it changes during development. To address these questions, we examined coupling at the cerebellar inhibitory basket cell (BC)-Purkinje cell (PC) synapse. Biophysical analysis of transmission by paired recording and intracellular pipette perfusion revealed that the effects of exogenous Ca2+ chelators decreased during development, despite constant reliance of release on P/Q-type Ca2+ channels. Structural analysis by freeze-fracture replica labeling (FRL) and transmission electron microscopy (EM) indicated that presynaptic P/Q-type Ca2+ channels formed nanoclusters throughout development, whereas docked vesicles were only clustered at later developmental stages. Modeling suggested a developmental transformation from a more random to a more clustered coupling nanotopography. Thus, presynaptic signaling developmentally approaches a point-to-point configuration, optimizing speed, reliability, and energy efficiency of synaptic transmission
Fungal infection alters collective nutritional intake of ant colonies
No full textIn animals, parasitic infections impose significant fitness costs.1,2,3,4,5,6 Infected animals can alter their feeding behavior to resist infection,7,8,9,10,11,12 but parasites can manipulate animal foraging behavior to their own benefits.13,14,15,16 How nutrition influences host-parasite interactions is not well understood, as studies have mainly focused on the host and less on the parasite.9,12,17,18,19,20,21,22,23 We used the nutritional geometry framework24 to investigate the role of amino acids (AA) and carbohydrates (C) in a host-parasite system: the Argentine ant, Linepithema humile, and the entomopathogenic fungus, Metarhizium brunneum. First, using 18 diets varying in AA:C composition, we established that the fungus performed best on the high-amino-acid diet 1:4. Second, we found that the fungus reached this optimal diet when given various diet pairings, revealing its ability to cope with nutritional challenges. Third, we showed that the optimal fungal diet reduced the lifespan of healthy ants when compared with a high-carbohydrate diet but had no effect on infected ants. Fourth, we revealed that infected ant colonies, given a choice between the optimal fungal diet and a high-carbohydrate diet, chose the optimal fungal diet, whereas healthy colonies avoided it. Lastly, by disentangling fungal infection from host immune response, we demonstrated that infected ants foraged on the optimal fungal diet in response to immune activation and not as a result of parasite manipulation. Therefore, we revealed that infected ant colonies chose a diet that is costly for survival in the long term but beneficial in the short term—a form of collective self-medication
Dynamically maintaining the persistent homology of time series
No full textWe present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right