Complexity Classes Research Articles

Performance and scaling analysis of variational quantum simulation

Abstract We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error tolerance. In a comparison against a non-variational method based on Trotterized time evolution, we observe a better scaling of the depth requirements using the VQS approach with respect to both the size of the system and the simulated time. Results are also put into perspective by discussing the corresponding classical complexity required for VQS. Our results allow us to identify a possible advantage region for VQS over Trotterization.

On Complexity Classes of Envy-Free Pricing Problems: A Short Survey

On Complexity Classes of Envy-Free Pricing Problems: A Short Survey

Application of a Cell-Free Synthetic Biology Platform for the Reconstitution of Teleocidin B and UK-2A Precursor Biosynthetic Pathways.

We report the successful cell-free reconstitution of two natural product biosynthetic pathways of divergent complexity and structural classes. We first constructed the teleocidin biosynthetic pathway using our BY-2 (tobacco) cell-free protein synthesis (CFPS) system. We discovered a direct interaction between TleA and MbtH, and showed that the BY-2 system is capable of producing more than 80 mg/L teleocidin B-3 with cofactor supplementation and ∼20 mg/L with no cofactors supplemented, demonstrating the high metabolic activity of the system. We then extended our methodology and report the first successful cell-free biosynthesis of UK-2 diol (precursor to the commercially valuable secondary metabolite UK-2A) from simple building blocks by refactoring a complex pathway of 10 proteins in the wheat germ CFPS system. We show that plant CFPS systems are suitable for reconstructing pathways and identifying the functions of uncharacterized genes linked to biosynthetic gene clusters and rate-limiting biosynthetic steps.

Mortality and survival rate in a scottish cohort of adults with congenital heart disease

Abstract Background Adult patients with congenital heart disease (ACHD) experience higher rates of morbidity and reduced long-term survival in comparison to the general population. The care of this cohort of patients requires specialist expertise which is mainly delivered at tertiary centers. Aims We aim to report the clinical characteristics, mortality rates and causes of death in a contemporary cohort of ACHD patients followed up in a North- East Scottish Health Board. Methods We prospectively followed up ACHD patients aged ≥17 years (n=645) under review at the Regional NHS ACHD Clinic in a North- East Scottish Health Board between the years 2020 and 2023. We recorded the number and the causes of death as documented on our electronic records and on correspondence with primary care physicians. Survival analysis was performed according to the 2020 ESC Guidelines classification of congenital heart disease complexity (Table 4) classes using Kaplan-Meier method with log-rank (Mantel-Cox) test done in IBM SPSS v.24. Results Our ACHD cohort (n=645, 54% females and 46% males) included patients of all three ESC complexity classes (30% mild, 60% moderate and 10% severe). Between 2020 and 2023, 18 patients (2.8%) died, with a total incidence of 0.93 deaths/100 patient years. Median age of death was 59 years (IQR 45–71), and the majority of deceased patients were males (56%). There were 2 deaths in the mild complexity group, 11 deaths in the moderate complexity group and 5 deaths in the severe complexity group (See Table 1). This was found to correspond to an incidence of 0.34, 0.95 and 2.64 deaths/100 patient years respectively. The leading causes of death were heart failure (28%) and malignancy (22%). Using Kaplan-Meier survival analysis we found that the survival distributions for the mild, moderate and severe ACHD complexity groups were statistically significantly different by log-rank test (χ2(2) = 11.47, p < .005) (See Figure 1). Patients with moderate ACHD complexity had a median survival age 67 years (95% CI 58.1-75.9), patients with severe ACHD had median survival age 57 years (95% CI 44.7-69.2). Median survival could not be calculated for the mild group due to lack of data points. Conclusion The ACHD patient group is characterised for a variety of pathophysiology and clinical presentations. They require lifelong medical input and in spite of the local and national expertise, the mortality and morbidity rates are still high. Heart failure was the leading cause of death in this cohort which is similar to previous reported data. Mortality rates were proportional to the complexity of the underlying ACHD diagnosis. The survival rate of patients in the severe complexity group was ten years less than the moderate complex group. ACHD patients in the moderate and severe complexity groups have significantly reduced life expectancy and require access and clinical expertise from National ACHD Specialty Centers.

Communication Complexity of Entanglement-Assisted Multi-Party Computation

We consider a quantum and a classical version of a multi-party function computation problem with n players, where players 2,…,n need to communicate appropriate information to player 1 so that a “generalized” inner product function with an appropriate promise can be calculated. In the quantum version of the protocol, the players have access to entangled qudits but the communication is still classical. The communication complexity of a given protocol is the total number of classical bits that need to be communicated. When n is prime, and for our chosen function, we exhibit a quantum protocol (with complexity (n−1)(logn) bits) and a classical protocol (with complexity ((n−1)2(logn2) bits)). Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols.

Surgical training trends in the Americas: A cross-continental assessment of minimally invasive surgery and open surgery among surgical trainees.

Minimally invasive surgery (MIS) has become standard of care in many high-income countries, but its adoption in low- and middle-income countries (LICs/MICs) has been impeded by resource- and training-related barriers. We hypothesized that trainees in MICs perform MIS procedures less often, and that as procedure complexity increases, the rate of MIS decreases. A 22-question survey, distributed to representative leaders across Latin America, collected country-specific graduating trainee case requirements and volumes for four index procedures (cholecystectomy, appendectomy, inguinal hernia repair, colectomy) using MIS or open surgery (OS). USA data was obtained from the Accreditation Council for Graduate Medical Education. Kruskal-Wallis and Mann-Whitney U tests were performed to determine whether the rate of MIS differed across all countries, procedure complexity classes, and high income countries (HICs)/MICs. Seven experts (70% response rate) completed the survey, representing: Brazil, Chile, Ecuador, Guatemala, Mexico, Panama, and Paraguay. The percentage of MIS completed by trainees varied with mean and interquartile ranges as follows: cholecystectomy (60%±54%), appendectomy (41%±69%), inguinal hernia repair (19%±23%), colectomy (16%±29%). There was a significant difference in mean MIS experience across the eight countries (H=17.6, p=0.014) and between most complex and least complex procedures (p=0.039). No difference was found between MICs and HICs (p=0.786). We found a significant difference of general surgery trainee exposure to MIS versus OS across the Americas, but the difference was not significantly associated with World Bank Income Groups. Different trainee experiences with MIS and OS may highlight an opportunity for international and bidirectional collaboration.

Multimodal and Multifactor Branching Time Active Inference.

Active inference is a state-of-the-art framework for modeling the brain that explains a wide range of mechanisms. Recently, two versions of branching time active inference (BTAI) have been developed to handle the exponential (space and time) complexity class that occurs when computing the prior over all possible policies up to the time horizon. However, those two versions of BTAI still suffer from an exponential complexity class with regard to the number of observed and latent variables being modeled. We resolve this limitation by allowing each observation to have its own likelihood mapping and each latent variable to have its own transition mapping. The implicit mean field approximation was tested in terms of its efficiency and computational cost using a dSprites environment in which the metadata of the dSprites data set was used as input to the model. In this setting, earlier implementations of branching time active inference (namely, BTAIVMP and BTAIBF) underperformed in relation to the mean field approximation (BTAI3MF) in terms of performance and computational efficiency. Specifically, BTAIVMP was able to solve 96.9% of the task in 5.1 seconds, and BTAIBF was able to solve 98.6% of the task in 17.5 seconds. Our new approach outperformed both of its predecessors by solving the task completely (100%) in only 2.559 seconds.

PRINCIPLES FOR PREPARATION OF GROUND AND DESIGN MODELS RELATED TO ROCK MASSES IN THE LIGHT OF THE SECOND GENERATION OF EUROCODE 7

The article gives elements of methodology for preparation of ground models related to rock masses in the light of the second generation of Eurocode 7 (EC7 2025). The goal is to present state of the art in this field and to discuss procedures in ground modelling for typical rock engineering problems. Proposed methodology is based on earlier knowledge in preparation of engineering geological and geotechnical models developed in Yugoslavia, modified and adopted to newer recomendations in the EC7 2025. Preparation of Ground and Geotechnical Design Model shall be based on results from geotechnical investigations necessary in succesful definiton of Geotechnical Categories (GC) based on a combination of Consequence Class (CC) and Geotechnical Complexity Class (GCC). Practical illustration is done through presentation of several case histories for different types of structures constructed in rock mass media along Macedonian road network or hydrotechnical projects. Some open questions that can be a starting point for further developments are also mentioned.

Uncloneable Quantum Advice

The famous no-cloning principle has been shown recently to enable a number of uncloneable cryptographic primitives, including the copy-protection of certain functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a computation, but that is natively unkeyed: quantum advice. Remarkably, this is an application of the no-cloning principle in a context where the quantum states of interest are not chosen by a random process. We establish unconditional constructions for promise problems admitting uncloneable quantum advice and, assuming the feasibility of quantum copy-protecting certain functions, for languages with uncloneable advice. Along the way, we note that state complexity classes, introduced by Rosenthal and Yuen (ITCS 2022) — which concern the computational difficulty of synthesizing sequences of quantum states — can be naturally generalized to obtain state cloning complexity classes. We make initial observations on these classes, notably obtaining a result analogous to the existence of undecidable problems. Our proof technique defines and constructs ingenerable sequences of finite bit strings, essentially meaning that they cannot be generated by any uniform circuit family with non-negligible probability. We then prove a generic result showing that the difficulty of accomplishing a computational task on uniformly random inputs implies its difficulty on any fixed, ingenerable sequence. We use this result to derandomize quantum cryptographic games that relate to cloning, and then incorporate a result of Kundu and Tan (arXiv 2022) to obtain uncloneable advice. Applying this two-step process to a monogamy-of-entanglement game yields a promise problem with uncloneable advice, and applying it to the quantum copy-protection of pseudorandom functions with super-logarithmic output lengths yields a language with uncloneable advice.

Unveiling Barriers and Challenges of AI Technology Integration in Education: Assessing Teachers’ Perceptions, Readiness and Anticipated Resistance

This study seeks to fill a gap in the literature concerning the extrinsic barriers that affect the integration of artificial intelligence (AI) technologies, such as ChatGPT, within the educational sphere. While previous studies have predominantly focused on intrinsic factors like teachers’ attitudes and beliefs, as well as the general benefits and drawbacks of AI in education, there has been limited investigation into how external obstacles, such as large class sizes, insufficient resources, slow internet connections, and outdated technology, affect this integration. The importance of this study lies in its assessment of whether these extrinsic barriers contribute to teachers' resistance to embracing AI technology. This study employs a quantitative method to explore this issue, using a questionnaire administered to thirteen (n=13) EFL instructors from the Department of English at Ibn Khaldoun University of Tiaret, Algeria. The results derived from this study reveal that while participants recognised AI's potential to improve student learning and expressed confidence in its integration, they also identified extrinsic barriers such as technical complexity, inadequate training, limited resources, and large class sizes as critical factors contributing to their resistance to incorporating AI tools into their teaching practices. This research emphasises the necessity of addressing these external barriers to better align technological innovations with teachers' needs and readiness, thereby enhancing the effective integration of AI in education.

Adaptive Distributed Control of Nonlinear Multiagent Systems With Event-Triggered for Communication Faults and Dead-Zone Inputs.

This article studies the containment control problem of nonlinear multiagent systems (MASs) subjected to communication link faults and dead-zone inputs. In case of an unknown fault in the communication link, there is no constant Laplacian matrix anymore and each follower agent cannot be informed of the global information simultaneously. To deal with this problem, an adaptive compensating estimator is constructed to estimate the signal spanned by the leaders. Instead of using the linear filter, a nonlinear filter is employed, which both solves the classical complexity explosion in the traditional backstepping method and flushes out the usefulness of the boundary layer error. Considering the dead zone input, we propose two event-triggered schemes, that is, the update-triggered scheme and the transmit-triggered scheme. In the former, the threshold function involves the tracking errors and additional dynamic variable, which can provide the desirable tradeoff between the containment control performance of the considered MASs and saving communication resources. In the latter, the triggered condition is designed according to the characteristic of dead zone, which makes the communication burden be reduced further. Following the backstepping design framework, an adaptive containment control is constructed, it is shown that the containment error can converge to an adjustable residual set even if MASs are subjected to the unknown and bounded communication link faults and dead-zone inputs. Finally, an example is given to show the effectiveness of the proposed results.

A PARAMETERIZED HALTING PROBLEM, TRUTH AND THE MRDP THEOREM

Abstract We study the parameterized complexity of the problem to decide whether a given natural number n satisfies a given $\Delta _0$ -formula $\varphi (x)$ ; the parameter is the size of $\varphi $ . This parameterization focusses attention on instances where n is large compared to the size of $\varphi $ . We show unconditionally that this problem does not belong to the parameterized analogue of $\mathsf {AC}^0$ . From this we derive that certain natural upper bounds on the complexity of our parameterized problem imply certain separations of classical complexity classes. This connection is obtained via an analysis of a parameterized halting problem. Some of these upper bounds follow assuming that $I\Delta _0$ proves the MRDP theorem in a certain weak sense.

Assembly Theory is an approximation to algorithmic complexity based on LZ compression that does not explain selection or evolution

We formally prove the equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression that belongs to the LZ family of popular compression algorithms. Such popular lossless compression algorithms behind file formats such as ZIP and PNG have been shown to empirically reproduce the results that AT considers its cornerstone. The same results have also been reported before AT in successful application of other complexity measures in the areas covered by AT such as separating organic from non-organic molecules and in the context of the study of selection and evolution. We demonstrate that the assembly index is equivalent to the size of a minimal context-free grammar. The statistical compressibility of such a method is bounded by Shannon Entropy and other equivalent traditional LZ compression schemes, such as LZ77 and LZW. We also demonstrate that AT, and the algorithms supporting its pathway complexity, assembly index, and assembly number, define compression schemes and methods that are subsumed into algorithmic information theory. We conclude that the assembly index and the assembly number do not lead to an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by (abiotic or biotic) selection and evolution, that could not have been arrived at using Shannon Entropy, or that have not been already reported before using classical information theory or algorithmic complexity.

Spiers Memorial Lecture: Quantum chemistry, classical heuristics, and quantum advantage.

We describe the problems of quantum chemistry, the intuition behind classical heuristic methods used to solve them, a conjectured form of the classical complexity of quantum chemistry problems, and the subsequent opportunities for quantum advantage. This article is written for both quantum chemists and quantum information theorists. In particular, we attempt to summarize the domain of quantum chemistry problems as well as the chemical intuition that is applied to solve them within concrete statements (such as a classical heuristic cost conjecture) in the hope that this may stimulate future analysis.

Quantum state synthesis: relation with decision complexity classes and impossibility of error reduction

This work investigates the relationships between quantum state synthesis complexity classes (a recent concept in computational complexity that focuses on the complexity of preparing quantum states) and traditional decision complexity classes. We especially investigate the role of the \emph{synthesis error parameter}, which characterizes the quality of the synthesis in quantum state synthesis complexity classes.We first show that in the high synthesis error regime, collapse of synthesis classes implies collapse of the equivalent decision classes. For more reasonable synthesis error, we then show a similar relationships for $\BQP$ and $\QCMA$. Finally, we show that for quantum state synthesis classes it is in general impossible to improve the quality of the synthesis: unlike the completeness and soundness parameters (which can be improved via repetition), the synthesis error cannot be reduced, even with arbitrary computational power.

Representing Matroids over the Reals is $\exists \mathbb R$-complete

A matroid $M$ is an ordered pair $(E,I)$, where $E$ is a finite set called the ground set and a collection $I\subset 2^{E}$ called the independent sets which satisfy the conditions: (i) $\emptyset \in I$, (ii) $I'\subset I \in I$ implies $I'\in I$, and (iii) $I_1,I_2 \in I$ and $|I_1| < |I_2|$ implies that there is an $e\in I_2$ such that $I_1\cup \{e\} \in I$. The rank $rank(M)$ of a matroid $M$ is the maximum size of an independent set. We say that a matroid $M=(E,I)$ is representable over the reals if there is a map $\varphi \colon E \rightarrow \mathbb{R}^{rank(M)}$ such that $I\in I$ if and only if $\varphi(I)$ forms a linearly independent set. We study the problem of matroid realizability over the reals. Given a matroid $M$, we ask whether there is a set of points in the Euclidean space representing $M$. We show that matroid realizability is $\exists \mathbb R$-complete, already for matroids of rank 3. The complexity class $\exists \mathbb R$ can be defined as the family of algorithmic problems that is polynomial-time is equivalent to determining if a multivariate polynomial with integers coefficients has a real root. Our methods are similar to previous methods from the literature. Yet, the result itself was never pointed out and there is no proof readily available in the language of computer science.

γ-clustering problems: Classical and parametrized complexity

We introduce the γ-clustering problems, which are variants of the well-known Cluster Editing/Deletion/Completion problems, and defined as: given a graph G, how many edges must be edited in G, deleted from G, or added to G in order to have a disjoint union of γ-quasi-cliques. We provide here the complete complexity classification of these problems along with FPT algorithms parameterized by the number of modifications, for the NP-complete problems. We also study here a variant of these problems where the number of final clusters is a fixed constant, obtaining mostly the same results regarding classical and parameterized complexity.

Weighted automata and logics meet computational complexity

Complexity classes such as #P, ⊕P, GapP, OptP, NPMV, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class NP[S] for a suitable semiring S, defined via weighted Turing machines over S similarly as NP is defined in the unweighted setting. Other complexity classes can be lifted to the quantitative world as well, the resulting classes relating to the original ones in the same way as weighted automata or logics relate to their unweighted counterparts. The article surveys these too-little-known connexions implicit in the existing literature and suggests a systematic approach to the study of weighted complexity classes. An extension of SAT to weighted propositional logic is proved to be complete for NP[S] when S is finitely generated. Moreover, a class FP[S] is introduced for each semiring S as a counterpart to P, and the relations between FP[S] and NP[S] are considered.

Impact of Malocclusions on Periodontopathogenic Bacterial Load and Progression of Periodontal Disease: A Quantitative Analysis.

(1) Periodontal disease (PD) is a globally prevalent chronic inflammatory condition, exacerbated by the dysbiosis of the oral microbiota. This study aims to evaluate the bacterial load of specific periodontopathogenic bacteria in patients with malocclusions (MAL) compared to those without. (2) Methods: Conducted at the "Carol Davila" University of Medicine and Pharmacy, Bucharest, Romania, this pilot study involved two groups: patients with MAL and PD, and patients with PD but without MAL. We included 20 patients: 10 with MAL (9 with crowding and 1 with an open bite) and 10 without MAL. Gingival crevicular fluid was collected for bacterial DNA extraction and quantified bacterial load using real-time PCR, focusing on 12 periodontopathogenic bacteria across different complexity classes. (3) Results: The study identified significantly higher concentrations of Treponema denticola (p = 0.023, median = 4.32, IQR = 2.76-5.53 vs. median = 1.93, IQR = 0-3.19), Tannerella forsythia (p = 0.020, mean = 6.04 ± 0.72 vs. mean = 4.4 ± 1.89) and Porphyromonas gingivalis (p = 0.002, median = 5.64, IQR = 4.94-5.98 vs. median = 2.48, IQR = 0-4.05) in patients with MAL compared to those without. This suggests that MAL contributes to an environment conducive to the proliferation of specific pathogens, potentially accelerating PD progression. Additionally, Eikenella corrodens (p = 0.040, mean = 4.55 ± 1.02 vs. mean = 3.23 ± 1.56), Campylobacter rectus (p < 0.001, mean = 4.2 ± 0.56 vs. mean = 1.8 ± 1.51), Prevotella intermedia (p = 0.043, median = 5.04, IQR = 0-5.49 vs. median = 0, IQR = 0-3.39), Capnocytophaga sputigena (p = 0.011, median = 5.91, IQR = 5.47-6.17 vs. median = 4.63, IQR = 3.83-5.64), and Capnocytophaga gingivalis (p = 0.007, median = 5.87, IQR = 5.34-6.03 vs. median = 4.4, IQR = 3.5-5.71) also showed elevated concentrations, indicating the broad impacts of MAL on oral microbial profiles. (4) Conclusions: The findings demonstrate a significant relationship between MAL and increased bacterial loads, underscoring the need for its integration in managing PD. Future research should expand demographic diversity and employ longitudinal designs to better understand the causative mechanisms at play.

The Temporal Evolution of Nonneutralized Electric Currents and the Complexity of Solar Active Regions

We study the evolution of electric currents during the emergence of magnetic flux in the solar photosphere and the differences exhibited between solar active regions of different Hale complexity classes. A sample of 59 active regions was analyzed using a method based on image segmentation and error analysis to determine the total amount of nonneutralized electric current along their magnetic polarity inversion lines. The time series of the total unsigned nonneutralized electric current, I NN,tot, exhibit intricate structure in the form of distinct peaks and valleys. This information is largely missing in the respective time series of the total unsigned vertical electric current I z . Active regions with δ-spots stand out, exhibiting a 1.9 times higher flux emergence rate and 2.6 times higher I NN,tot increase. The median value of their peak I NN,tot is equal to 3.6 × 1012 A, which is more than three times higher than that of the other regions of the sample. An automated detection algorithm was also developed to pinpoint the injection events of nonneutralized electric current. The injection rates and duration of these events were higher with increasing complexity of active regions, with regions containing δ-spots exhibiting the strongest and longest events. These events do not necessarily coincide with increasing magnetic flux, although they exhibit moderate correlation. We conclude that net electric currents are injected during flux emergence but are also shaped drastically by the incurred photospheric evolution as active regions grow and evolve.