**1. Introduction**

In its first appearance, the Weibull distribution [1] claimed its wide applicability. Survival analysis, reliability engineering, and extreme value theory are some of its applicability. To amplify the relevance of the Weibull, a regression structure is added to one of the parameters, i.e., the behavior of the distribution may be explained from covariates (explanatory variables) and unknown parameters to be estimated from observable data.

In statistical inference, it is often desirable to test if there are regression parameters statistically significant and the Wald test is commonly performed. Under standard regularity conditions, the null distribution of the Wald statistic is asymptotically chi-squared, a consequence of the maximum likelihood estimators (MLE) distribution. Therefore, the Wald test must be avoided if the sample size is not large enough, because the distribution of the MLE will be poorly approximated by the normal distribution.

Preventing the complexity of the statistical tests, the skewness coefficient (say *γ*) of the distribution of the MLE is an easy way to verify if the approximation to normality is adequate. A value of *γ* far from zero indicates a departure from the normal distribution. Pearson's standardized third cumulant defined by *γ* = *κ*3/*κ*3/2 2 , where *κr* is the *r*th cumulant of the distribution, is the most well-known measure of skewness. When *γ* > 0 (*γ* < 0) the distribution is positively (negatively) skewed and will have a longer (shorter) right tail and a shorter (longer) left tail. If the distribution is symmetrical, *γ* equals zero. However, there are in [2] (Exercise 3.26) asymmetrical distributions with as many zero-odd order central moments as desired, so, the value of *γ* must be interpreted with some caution.

In the statistical literature, there is not a closed-form for the skewness coefficient of *γ* of the MLE in several regression models. Ref. [3] obtained a general *n*−1/2 *γ* expression (say *γ*1) for the distribution of the MLE, where *n* is the sample size. Following [3], several works have been developed in order to obtain the *γ*1 coefficient. In the first, Ref. [4] determined its expression for the class of generalized linear models and, the last one, Ref. [5] defined the *γ*1 for the varying dispersion beta regression model and showed that this coefficient for the distribution of the MLE of the precision parameter is relatively large in small to moderate sample sizes. This paper is the first focused on a censored model.

In this work, we derive the *γ*1 coefficient of the distribution of the MLE of the linear parameters in the Weibull censored data, assuming *σ* known, as *σ* = 1/2 and 1, the Rayleigh and exponential models, respectively. We discuss the situation when *σ* is unknown, however, it can be replaced by a consistent estimator, and then we can turn back to the original situation. This type of procedure was performed, for instance, by [4].

The remainder of the paper is organized as follows. Section 2 defines the Weibull censored data. In Section 3, we obtain a simple matrix expression, of order *n*−1/2, for the skewness coefficients of the distributions of the MLEs of the linear regression parameters. In Section 4, some Monte Carlo simulations are performed. Two applications are presented in Section 5. Concluding remarks are offered in Section 6.

### **2. The Weibull Censored Data**

We say that a continuous random variable *T* has Weibull distribution with scale parameter *θ* and shape parameter *σ*, or *T* ∼ WE(*θ*, *σ*), if its probability density function (pdf) is given by

$$f(t; \theta, \sigma) = \frac{1}{\sigma \theta^{1/\sigma}} t^{1/\sigma - 1} \exp\left\{-\left(t/\theta\right)^{1/\sigma}\right\},\tag{1}$$

with *t* > 0, *σ* > 0 and *θ* > 0. From (1), we can observe two particular distributions: the exponential and the Rayleigh, where *σ* = 1 and *σ* = 1/2, respectively. In lifetime data, there is the censoring restriction, i.e, if *T*1, ... , *Tn* are a random sample from (1), instead of *Ti*, we observe, under right censoring, *ti* = min(*Ti*, *Li*), where *Li* is the censoring time, independent of *Ti*, *i* = 1, ... , *n*. In this work, we consider an hybrid censoring scheme, where the study is finalized when a pre-fixed number, *r* ≤ *n*, out of *n* observations have failed, as well as when a prefixed time, say *L*1 = ... = *Ln* = *L*, has been reached. The type I censoring is a particular case for *r* = *n* and the type II censoring appears when *L*1, ... , *Ln* = + ∞. Additionally, we add the non-informative censoring assumption, i.e., the random variables *Li* does not depend on *θ*. Under this setup, the log-likelihood function has the form

$$L(\theta, \sigma) \;= \left(\sigma \theta^{1/\sigma}\right)^{-r} \exp\left\{ \left(\frac{1}{\sigma} - 1\right) A\_1 - \frac{1}{\theta^{1/\sigma}} A\_2 \right\},$$

where *r* = ∑*n i*=1 *δi*, *A*1 = ∑*n i*=1 *δi* log *ti*, *A*2 = ∑*n i*=1 *t*1/*σ i* , *δi* = 1, if *Ti* ≤ *Li* and *δi* = 0, otherwise. Usually, the regression modeling considers the distribution of *Yi* = log(*Ti*) instead of *Ti*. The distribution of *Yi* is of the extreme value form with pdf given by

$$f(y\_i; \mathbf{x}\_i) = \frac{1}{\sigma} \exp\left\{ \frac{y\_i - \mu\_i}{\sigma} - \exp\left(\frac{y\_i - \mu\_i}{\sigma}\right) \right\}, \quad -\infty < y\_i < \infty \tag{2}$$

.

where *μi* = log *θi*. The regression structure can be incorporated in (2) by making *θi* = exp *x i β* , where *β* is a p-vector of unknown parameters and *xi* is a vector of regressors related to the *i*th observation. From this moment, we assume that *σ* is known, then, the log-likelihood function derived from (2) is given by

$$\ell(\mathcal{J}) = \sum\_{i=1}^{n} \left[ \delta\_i \left( -n \log \sigma + \frac{y\_i - \mu\_i}{\sigma} \right) - \exp \left( \frac{y\_i - \mu\_i}{\sigma} \right) \right]$$

The total score function and the total Fisher information matrix for *β* are, respectively, *Uβ* = *σ*−1*XW*1/2*v* and *Kββ* = *σ*−2*XW X*, where *X* = (*x*1, ... , *xn*), the model matrix, assuming rank (*X*) = *p*, *W* = diag(*w*1, ... , *wn*), *wi* = E exp *yi*−*μi σ* and *v* = (*v*1, ... , *vn*), *vi* = )−*δi* + exp *yi*−*μi σ* \* *w*−1/2 *i* . It can observed that the value of *wi* depends on the mechanism of censoring. That means *wi* = *q* × 1 − exp )−*L*1/*σ i* exp(−*μi*/*σ*)\* + (1 − *q*) × (*r*/*n*), where *W*(*r*) denotes the *r*th order statistic from *W*1, ... , *Wn* and *q* = P *W*(*r*) ≤ log *Li*. Note that *q* = 1 and *q* = 0 for types I and II censoring, respectively. The proof is presented in the Appendix A. The MLE of *β*, *β* , is the solution of *Uβ* = **0**. The *β* can not be expressed in closed-form. It is typically obtained by numerically maximizing the log-likelihood function using a Newton or quasi-Newton nonlinear optimization algorithm. Under mild regularity conditions and in large samples,

$$
\widehat{\boldsymbol{\theta}} \sim \operatorname{N}\_p \left( \boldsymbol{\beta}, \boldsymbol{\mathsf{K}}\_{\boldsymbol{\theta}\boldsymbol{\beta}}^{-1} \right),
$$

 ,

approximately.


**2. Modelling**

An alternate approach to mitigate the hazardous effects of earthquakes is based on a consid‐ eration of the distribution of energy within a structure. The input energy from the ground acceleration is transformed into both kinetic and potential (strain) energy that must be either absorbed or dissipated trough heat. A large portion of the input energy, instead of being absorbed by hysteretic action (i.e. damage of the structure) can be dissipated with supple‐

This approach to seismic energy dissipation is made clear by considering the following time‐

where *E* is the absolute energy input from the earthquake motion, *E*k is the absolute kinetic energy, *E*s is the elastic (recoverable strain energy), *E*h is the irrecoverable energy dissipated by the structural system through inelastic or other forms of action (hysteretic or viscous), *E*d is the

The chapter analyses the seismic retrofit of an existing viaduct, by assessing an actually designed case study. The viaduct at issue, built during the Seventies, serving a fast‐moving thoroughfare in the city of Naples (Italy), features reinforced concrete piers and a mixed steel‐ concrete box deck. Three solutions, corresponding to the most common types of interventions for earthquake protection, have been compared: the first by using hydraulic dissipation devices, the second using sliding pendulum isolator devices and the third by using elastomeric isolators. The differences have been compared according to traffic interferences, interferences with existing structures, operational needs and to time and costs necessary to achieve a final

The viaduct analysed, which already has an earthquake intervention in place, features a length of 1360m and a continuous deck on 18 spans with variable clearance from 62 to 92m, separated by four longitudinal joints, implemented with Gerber saddles to assure structural continuity (**Figures 1** and **2**). The reinforced concrete piers have a hollow circular section, with a variable base diameter ranging from 2.65 to 3.30m. They are vertically compressed and feature a variable height ranging from 7.90 to 38.80m. The foundations are deep, well and raft based with piles. The structural joints are located at the piers 4, 6, 11 and 14. One particular aspect of the viaduct is that there is only one support per each pier, placed at the central part of the box. Hence, the deck is balanced, since the two adjacent runways are connected by means of

Intervention on an existing work always requires special attention and a meticulous study. For example, with the viaduct under examination, the base of the piers is inaccessible for any type of reinforcement intervention. Additionally, it is not possible to stop traffic in order to replace the supports, and therefore, it is not possible to work on the abutments, to draw back the ballast retainers if a larger gap than the present one (measuring 15 cm) should be required. Moreover,

energy dissipated by a supplemental damping system and *t* represents the time.

( ) () () () () *Et E t E t E t E t* =+++ *k zhd* (1)

mental systems.

130 Structural Bridge Engineering

project solution.

**1.1. The viaduct main features**

transverse girders at each support section (**Figure 3**).

dependent conservation of energy relationship:

The analyses have been carried out using a finite‐element analysis software on a model, consisting in mono‐dimensional elements; they are non‐linear with step‐by‐step integration of the equations of motion.

For seismic purposes, the following parameters (Italian Standard DM 14.01.2008 [1, 2]) have been taken into account:

**•** Topographic coefficient *T*1=1 that correspond to a flat surface.

**Figure 4.** Artificial accelerogram.

For the analysis, artificial spectrum‐compatible accelerograms have been used (**Figure 4**). It is noted that the use of real accelerograms and spectrum‐matching techniques, together with records selection tools, tends to be recommended for the derivation of suits of records for use in non‐linear dynamic analysis of structures but in this case, the access to real accelerograms was challenging. In literature [3], it is shown that the structural response estimated by using simulated records generally matches the response obtained using recorded motions. The software can generate artificial time‐histories of ground acceleration compatible with the target spectrum and gives a comparison between its response spectrum and the target spectrum itself (**Figure 5**).

The computational analysis has been carried out using finite‐element method. The model of the viaduct is three‐dimensional (3D) type (**Figure 6**), representing the stiffness features of the structural elements. The composing elements are all of linear elastic type, except for the restraint devices and for the base of the piers, where it is assumed that plastic hinges may form. It takes into account geometric and material non‐linearity.

**Figure 5.** Compatibility between response spectrum and target spectrum.

**Figure 6.** Finite‐element model.

**•** Rated life of the work: *V*N = 50 years, relative to bridges and infrastructures;

munication ways available;

132 Structural Bridge Engineering

**Figure 4.** Artificial accelerogram.

itself (**Figure 5**).

*S* wave in the first 30 m) range is 180—360 m/s;

**•** Topographic coefficient *T*1=1 that correspond to a flat surface.

**•** Use coefficient: *C*U = 2, corresponding to Use Class IV about strategic construction in case of calamity and bridges of particular importance after seismic events in order to keep com‐

**•** Reference life of the work equals to *V*R=100 years; it comes from the product *V*R = *V*N·*C*U;

**•** Soil type C: deposits of medium thickened soil, with layers of more than 30m where mechanical properties gradually increase with depth; VS30 (average equivalent velocity of

For the analysis, artificial spectrum‐compatible accelerograms have been used (**Figure 4**). It is noted that the use of real accelerograms and spectrum‐matching techniques, together with records selection tools, tends to be recommended for the derivation of suits of records for use in non‐linear dynamic analysis of structures but in this case, the access to real accelerograms was challenging. In literature [3], it is shown that the structural response estimated by using simulated records generally matches the response obtained using recorded motions. The software can generate artificial time‐histories of ground acceleration compatible with the target spectrum and gives a comparison between its response spectrum and the target spectrum

The computational analysis has been carried out using finite‐element method. The model of the viaduct is three‐dimensional (3D) type (**Figure 6**), representing the stiffness features of the structural elements. The composing elements are all of linear elastic type, except for the restraint devices and for the base of the piers, where it is assumed that plastic hinges may form.

It takes into account geometric and material non‐linearity.

For the piers, a moment‐curvature constitutive law has been adopted by using the Takeda model [4]. The model represents the hysteretic features of reinforced concrete structures by means of the trilinear relation force‐displacement, where the non‐linearity is modelled by using concentrated plastic hinges and takes into account cracking and yielding. From the force‐ displacement law, it is possible to retrieve the corresponding moment‐curvature link. Such assessment has been carried out distinctly for each pier. With this choice, it is possible to assess in the transient state the stiffness change of the substructures, checking the consequent re‐ distribution of the stresses among the following piers of the viaduct.

The support and restraint devices are represented by special elements where it is possible to specify stiffness in any of six degrees of freedom between two nodes. They do not behave like a standard beam element; the degrees of freedom are user specified and are independent of each other. For non‐linear analysis, each stiffness value may be defined via a non‐linear table: force‐velocity type for hydraulic devices and force‐displacement type for isolators.

The foundations of the piers and of the abutments are modelled with punctual restraints.


**Insights into the Genetic Architecture of Bran Friability and Water Retention Capacity, Two Important Traits for Whole Grain End-Use Quality in Winter Wheat**

### **Sviatoslav Navrotskyi 1, Vikas Belamkar 2,\*, P. Stephen Baenziger 2 and Devin J. Rose 1,2,\***

Received: 27 June 2020; Accepted: 21 July 2020; Published: 23 July 2020

**Abstract:** Bran friability (particle size distribution after milling) and water retention capacity (WRC) impact wheat bran functionality in whole grain milling and baking applications. The goal of this study was to identify genomic regions and underlying genes that may be responsible for these traits. The Hard Winter Wheat Association Mapping Panel, which comprised 299 lines from breeding programs in the Great Plains region of the US, was used in a genome-wide association study. Bran friability ranged from 34.5% to 65.9% (median, 51.1%) and WRC ranged from 159% to 458% (median, 331%). Two single-nucleotide polymorphisms (SNPs) on chromosome 5D were significantly associated with bran friability, accounting for 11–12% of the phenotypic variation. One of these SNPs was located within the *Puroindoline-b* gene, which is known for influencing endosperm texture. Two SNPs on chromosome 4A were tentatively associated with WRC, accounting for 4.6% and 4.4% of phenotypic variation. The favorable alleles at the SNP sites were present in only 15% (friability) and 34% (WRC) of lines, indicating a need to develop new germplasm for these whole-grain end-use quality traits. Validation of these findings in independent populations will be useful for breeding winter wheat cultivars with improved functionality for whole grain food applications.

**Keywords:** wheat quality; wheat milling; wheat hardness; puroindolines; water absorption capacity


In the twenty-first century, the government, especially the Ministry of Defence, also played a major role in planning and financing high-tech R&D, including in priority areas such as AI. However, as dictated by the character of new and emerging technologies, more emphasis was placed on the construction of civil-military, in particular business-state, relations under the direct leadership of the Russian state. Russia was characterized as a *quasi-capitalist* developmental state. Although market mechanisms did find their way into the Russian economy and innovation ecosystem following the end of the Cold War, several shortcomings were brought to attention: the reluctance of the government to ease its tight control over the economy, as expressed in direct control over business activities or government ownership; a proportionally greater emphasis on the military industry; as well as the backwardness of the civilian sector and its further weakening in light of the new round of sweeping Western sanctions imposed on Russia in response to its invasion of Ukraine in 2022. All of the above clearly demonstrates that exploratory experimentation has traditionally been constrained in Russia by the primacy of military science over technological sophistication and tight government control over innovation.

#### **6.1.6 Symbolic Innovation**

There is still one more extremely important aspect of the Russian cultural approach to innovation in the military-technological domain. Bringing the sophistication of Russia's military technology and equipment to the level of Western analogues has often had not only practical but also symbolic value for Russia. One of the key motives behind this endeavour has typically been Russia's obsession with its status as a great power, though in purely military terms. In particular, Russia's catch-up tendencies in its permanent arms race with the West have been driven, historically, by the objective of restoring that great power status, either challenged or lost as a result of impressive leaps forward in military technology made by its Western counterparts. For example, Russia was certainly a great power, at least from a narrow realist perspective, up until the mid-nineteenth century. Not only did the Crimean War expose Russia as a technologically inferior military, but it also seriously undermined Russia's international prestige and greatness. The narrative that Russia would not be satisfied by anything less than returning to the ranks of other major European powers accompanied the re-armament process in the late nineteenth century.

Similarly, the Soviet atomic project carried a great deal of symbolic significance in the twentieth century. The Soviet Union came out most clearly as the country that possessed great power in the aftermath of World War II. To be more precise, two major powers, the US and the USSR, and a rigid bipolar system emerged from World War II. Yet the atomic bombings of Hiroshima and Nagasaki were perceived by Soviet military experts as America's effort to strengthen its position vis-à-vis the USSR. One of the key motives behind the Soviets' own nuclear weapons programme, as archival records show, was to regain its status of a world power and an equal of the US. Only with its own nuclear weapons capability did the Soviet Union reemerge as a superpower on par with the US.

The process of military-technological innovation moved basically along the same track in the third case study. America appeared as the world's only superpower after the dissolution of the Soviet Union and the end of the Cold War, and the revival of Russia as a great power, even a superpower, has been one of the key narratives underlying the ongoing modernization of military equipment. One finding concerning the relationship between Russia's great power status and its arms industry deserves particular mention. The tsar, being unable to bring the domestic arms industry on equal footing with the industrialized countries in a relatively short period after the Crimean War, sought to reassert the country's great power status by ordering cutting edge weapons from abroad. This approach has fundamentally changed. For modern Russia, its position as a first-tier arms producer and supplier is one of the key attributes of its great power status.

To sum up, Russia has often been driven by symbolic motivations in its military-technological innovation. Before its status could be reasserted at the level of military technology, it was to be maintained through diplomacy, and in particular through slowing down, if not reversing, the technological advancements of Russia's potential adversaries. This is where the symbolic function of arms control and disarmament for Russia becomes apparent, in addition to other possible motivations discussed above. What is particularly interesting is that Russia's motivation for its pursuit of the leadership role in nineteenth-century disarmament negotiations was, inter alia, a way to compensate for its declining military power in the aftermath of the Crimean War and recover its status as a great power with influence over European affairs by means other than direct military competition.

What relates closely to the above discussion and deserves separate note is the symbolic construction of military parades in Russia. The significance of these symbolic displays of military might has been in boosting the image of Russia as a major military power both at home and abroad. To be even more precise, military parades have proved particularly useful in creating an idealized image of the Russian army, not always mirroring objective reality. For example, Russia's War Minister (1861–1881) Miliutin, as cited in Chapter 3, voiced the following critique against the general condition of the country's military: 'Everything is just great for parades, and just terrible for war' (cited in Panaeva 1986: 232). This became immediately obvious during the Crimean War. Miliutin's judgement is not necessarily representative in a historical perspective, but it draws attention to the gap that may exist between reality and its representation in countries obsessed with military parades such as Russia. Russia's military invasion of Ukraine in 2022 testifies to the lasting relevance of Miliutin's prophecy. Russia has indeed put to use some of its most advanced and sophisticated weapons in Ukraine (*Lenta* 2022a). So the situation is different from the one Russia found itself in in the mid-nineteenth century. However, the proportion of high-tech weapons and equipment is much higher when displayed during military parades than when actually deployed on the battlefield. The fact that Russia still has not used, at least at the time of writing, some of its latest weapon systems previously showcased in military parades (e.g. the T-14 Armata battle tank) in its major military operation in Ukraine also points to the existence of parade-only weapons in Russia.22 It would be fair to note

22 A few caveats are important to explain why the Armata is listed as an example. The Armata became one of the participants in the Victory Parade in 2015. During its military tests in the territory of Syria, 'a number of problematic solutions were identified regarding the level

that it is not only in Russia that some of the cutting-edge weapons end up being a demonstration of capabilities and do not get produced in the quantities generally required to make a difference. Gorenburg (Interview no. 8) mentioned America's B-1 bombers and Seawolf-class submarines as examples. The key difference is that the US does not proudly parade these weapons. Having also indicated that the Armata has been paraded years before becoming a fully operational combat vehicle, Galeotti (Interview no. 7) believed, however, that Russian military parades have become 'more honest' than they were in the past.23

#### **6.1.7 Manpower-Balanced Innovation**

Another key finding to emerge from this study is that, from the Russian perspective, the human-technology relationship has changed significantly, but not fundamentally, over the last hundred and fifty years. On the one hand, there has been a growing appreciation for the role of technology. As it comes across clearly in the arguments of Russian military experts, manpower-intensive approaches to warfare are being gradually replaced with technology-intensive ones. In the nineteenth century, there was a deep distrust of technology in Russian military circles, even though the growing role of technology was carefully recognized. The popular idea at that time was that the lack of military equipment or the inability to master it could be compensated for by the personnel's physical strength, high morale, and psychological preparation. However,

of sensitivity of the incoming projectile detection system, the optical-location complex, and the power plant,' according to Russian sources (Orlov 2021). One of the Russian language sources refers to a Chinese source, itself citing information from the Americans, to report that five Armata tanks were deployed in the Syrian province of Latakia, with three being allegedly hit by TOW-2B ATGMs and one completely destroyed (*Reporter* 2020). Nevertheless, Armata tanks were paraded through the Red Square in 2022. Besides their seeming immaturity, limited availability, and high production costs, Russia's reluctance to deploy T-14s in Ukraine may also be explained by the desire to avoid bad publicity in case something goes wrong again. The reputation of weapons for export purposes matters within Russia's military-oriented entrepreneurial model, as demonstrated in the example of Kalibr missiles in Chapter 5. At the same time, Russia's willingness to parade them even now may be explained by the intention to stir up foreign interest in these weapons systems, especially as T-14s are still under development and intended for export after the Russian army acquires them (*Interfax* 2021b). It clearly appears that maintaining the image of a first-tier producer and supplier of high-tech weaponry has high symbolic value for Russia. In general though, a military parade of this kind is not only a demonstration of technological advancement, but also a historical legacy for Russia, according to Galeotti (Interview no. 7).

23 The interview was conducted prior to February 2022.

the idea of overcoming technological disadvantages solely through the quality of manpower was slowly losing its appeal with the introduction of more advanced technologies and a gradual reduction in manpower. In the mid- to late- twentieth century, Soviet military experts admitted that technology was receiving an increasing share in the human-machine nexus. Progress in advanced automation and robotics gave rise to more ambitious hopes for the full robotization of military operations in twenty-first-century Russia.

On the other hand, many Russian experts believe that the role of humans in war does not decrease with time, but actually increases in direct relation with the increasing importance given to technology. One clue that may help explain the paradox of the still growing role of humans when martial skills are being gradually replaced by technology is the dichotomy between quantity and quality. The shift has, according to Russian military analysts, consisted of the declining role of massive armies and the increasing importance of highly trained troops equipped with the latest technology. In fact, this idea has its roots in the nineteenth century. It was already then that special emphasis was placed upon training designed to improve technical and combat skills of military personnel. The ever-increasing complexity of military equipment, especially in this day and age, may be one of the reasons for Russia's gradual transition from a conscript army to a professional army. However, as discussed in detail in Chapter 5, there is a gap between the discourse on mastering the latest technology and the practice of the Russian way of war in Ukraine. Low recruitment standards, demonstrated by the Russian(-led) forces in 2022, seriously challenge Russia's claims to military professionalism.

At the same time, emphasis on the supposed high morale qualities of the Russian troops has never been abandoned, as demonstrated by the elite discourse on the Russo-Georgian War and the conflict in eastern Ukraine. The use of this discourse as a morale booster may well serve as a negative function of technological sophistication and a propagandist compensation for the lack of obvious technological edge and technical skill. While technology has been an emerging factor in Russian military thinking, the idea of *expendable* manpower remains fairly constant. In addition to this, there is another relatively constant feature. While Russia's armed forces have traditionally been dominated by Slavs, in particular Russians, there have been marked increases in the percentage of recruits being drawn from ethnic minorities in war time (Curran and Ponomareff 1982; Daugherty 1993). This tendency was clearly seen again from the start of Russia's military invasion of Ukraine in 2022.

#### **6.2 Asymmetric Balancing and Further Contributions**

The above-mentioned characteristics constitute the Russian style of military-technological innovation, previously underexplored and sometimes even misunderstood. The key finding is that this style has displayed striking continuity over the centuries. In addition to filling this gap, the analysis presented in this book has a number of issue-specific contributions, and each of these deserves separate note.

First of all, this book contributed to a better understanding of the Russian theorization of strategic culture. The key finding was that it builds primarily upon the first generation of strategic culture scholarship in the West. Most importantly, this book showed, referring to trusted archival records, that these were Soviet military experts that introduced the concept of RMA. The existing literature often discusses their contribution in the context of the Soviet concept of MTR. However, it is a mistake to claim that these were Pentagon officials that broadened the Soviet-sourced concept of MTR to RMA. Drawing distinctions between these two terms based on the country of their origin is inherently flawed. This book distinguishes between them on the basis of Soviet original definitions of both, accompanied by corresponding Western definitions of the same.

Another contribution lies in capturing the way Soviet and Russian military experts have traditionally conceptualized revolutionary technology. One caveat applies. This is something that could not be foreseen immediately, at the level of theory, but came out very clearly of the subsequent empirical analysis. Four revolutionary qualities have been recorded and discussed extensively in Russian military circles in relation to each category of revolutionary weapons: their increased *destructiveness*, increased *speed* of their fire, increased *accuracy*, and increased *range*. Russian military experts often discussed new-generation weapons of increasing range, both nuclear missiles and high-precision longrange conventional weapons, in terms of their depth of strikes. This is where they recall the Soviet theory of 'deep battle' or 'deep operations'. This finding contributes to a better understanding of the technological parameter of RMA, especially as the existing body of knowledge about revolutionary technologies is still scarce (Hynek and Solovyeva 2022: 31). At the same time, it gives hints as to how technology-led RMAs, for example the current AI-RMA, should be studied as seen through Russian eyes.

Besides novel theoretical insights, this book offered two important side contributions with respect to the Soviet period in particular. First, archival data revealed that it would be a mistake to claim, as some Western analysts do, that the Soviets did not think in terms of Mutual Assured Destruction during the Cold War. Even though they did not use the phrase, Soviet political leaders and military experts recognized very clearly that the US and the USSR could destroy each other in a nuclear exchange regardless of who committed to strike first. Second, it was found, contrary to some existing literature, that the Soviet Union never had its own strategy of flexible response analogous to that of the US and NATO. The Soviets did indeed reach a point during the Cold War, at approximately the same time as the US, when they admitted that an initial conventional phase in a superpower war was possible. But they never accepted the possibility of a limited nuclear exchange in Europe. They criticized the American view of flexible response and even rejected the term itself.

From a more general perspective, the contribution of this book to International Relations and Strategic Studies literature lies in demonstrating the insufficiency of the neorealist school of thought to grasp the catch-up character of military-technological innovation in Russia. Realist explanations of Russian behaviour have arguably been most common in Western literature (e.g Lynch 2001; D'Anieri 2019; Feinstein and Pirro 2021; Tsygankov 2022). However, this approach has its shortcomings and this book demonstrated them in the example of the Russian approach to military-technological innovation. The original Waltzian account of neorealism and his 'balance of power' thesis (Waltz 1979) capture Russia's infinite quest for (re)arming, aimed at maintaining parity with – and rarely superiority over – its competitors. It also explains the fact that Russia's waves of military-technological innovation would, as a rule, coincide with the periods of shifting power balances and not in its favour. However, this approach fails to capture the nuances. First of all, it misses the key point: Russia's response to the competitive edge gained by its adversaries was not about restoring the balance per se. Having taken a cultural-historical approach (rather than a deductive-structural one) this book systematically demonstrated that Russia's catch-up tendencies were strongly linked to its claims to great power status. This research showed that possessing cutting edge technology had important symbolic value for Russia, including for the purpose of constructing the country's image as a first-tier producer and supplier of high-tech weaponry. Even if Russia struggled to compete in terms of quantity, it was unimaginable for the leadership in Moscow to give up on the very fact of possessing top-of-the-line military equipment, on par with the most advanced technological powers in the West.

Neoclassical realists, arguing that systemic pressures are always 'filtered' through decision-makers' perceptions, would explain this side of the problem better (Rose 1998: 157). However, there is still more to Russian symbolism than the realist school can accommodate. One of these aspects is the Russian culture of military parades, which do not always accurately reflect reality. In principle, it represents an act of balancing *through signals* and downgrades the notion of balancing, inter alia, to the level of a political message. On a more trivial note, Russia's reaction to shifting balances of power has almost never been immediate or automatic. There would usually be a time lag between a forward leap by Russia's competitors, typically in the West, and the Russian state's respective response. Moreover, this delay was not only a temporal gap between action and reaction. There would always be a trigger for Russia to initiate its own innovation cycle, typically a violent conflict – and often more than one – most clearly revealing its technological backwardness. Walt's (1987) 'balance of threat' theory, another variant of structural realism maintaining that one's balancing behaviour is determined by the threats one perceives, may well explain this. Besides building on its own military-technological failures, Russia often initiated innovation processes after the revolutionary impact of new-generation weapons was tested and proven in a violent conflict between other states. But even in these cases the technologically superior side would typically be represented by its own competitors and Russia would immediately be pushed to evaluate the consequences of a possible armed collision with them. However, Walt's original thesis maintains that states facing an external threat 'will align with others' against it (Walt 1987: 32). This argument is barely applicable to Russia. 'Russia has only two allies – its Army and its Navy', Alexander III used to say, and President Putin referred to this statement in his own speeches (*Lenta* 2022b). Later, Walt (2018) was more explicit about the fact that states may react to threats 'either by seeking allies or by building up their own capabilities'.

Nevertheless, the realist school of thought cannot fully capture Russia's *asymmetric balancing*. For example, one of the historical incidents going beyond the realist logic is Imperial Russia's effort to compensate for the loss of military power through the pursuit of global political leadership within the realm of humanitarian disarmament. This case represents an act of balancing *through diplomacy*, particularly through the construction of Russia's image as a culturally, if not militarily, superior nation. Besides diplomatic balancing, Russia has often engaged in other asymmetric balancing strategies, and not necessarily at the level of technology and military capabilities. For example, the supposed spiritual superiority of the Russian soldier was an illustration of Russia's balancing against the technological superiority of adversaries *through the art of fighting* in the nineteenth century. All of this goes beyond the traditional limits of the realist school of thought. Offering an open-ended and reflexive conceptual framework, this book captured exogenous influences as well as a complex mix of indigenous motivations and internal processes. As it showed, the realist logics may help explain a lot of the nuances but they fail to grasp Russia's approach to military-technological innovation in its cultural-historical complexity. This is largely due to the fact that nineteenth-century dynamics are often ignored by International Relations and Strategic Studies scholars, who focus primarily on the Cold War and the post-Cold War periods.

On a final note, this book was written with the hope of contributing to reducing the current gap between the Western representation of Russian military thought and what it has really been about. In doing so, it tried to avoid the orientalist image of Russian military strategy. While accepting the possible limitations of relying primarily on Soviet and Russian archives, the author considered it to be the most productive way to represent the inter-subjective Russian (and Soviet) understanding of military technology. At the same time, however, the critical perspective was maintained throughout the text and to the author's best knowledge. One caveat for prospective critiques of the approach is important. Since the discourse in the country's main military-theoretical journal is not originally intended for a foreign audience and not readily available in open access, it has often maintained a critical tone. Whenever deemed appropriate and possible, this book juxtaposed and balanced Russian sources with Western expert opinions.

### Summary

This book traces the dynamics of military-technological innovation in Russia over the last hundred and fifty years. The analysis relies extensively on primary data obtained from Russian archives, complemented by a series of expert interviews. The goal is to understand whether and to what extent Russia's respective discourses and practices constitute a distinct strategic cultural approach to military-technological innovation. From an empirical standpoint, the analysis is guided by six substantial arguments derived from the existing literature on Russian strategic culture, technology and military doctrine, interviews conducted by the author, and partially from the author's own knowledge of the problematic. In theoretical terms, this book offers and graphically nuances a novel conceptual model, theorizing processes related to military-technological innovation and the role of strategic culture. The last two arguments guiding the empirical focus of this research are derived from the theoretical discussion. This model is applied to three case studies, with the key findings represented graphically at the end of each chapter: the introduction of rifled breech-loading weapons in Imperial Russia in the nineteenth century, the invention of nuclear weapons in the Soviet Union in the twentieth century, and the development of precision-guided weapons in post-Soviet Russia in the twenty-first century. The findings, which identify the existence of a distinctive Russian strategic culture of military-technological innovation in a long-term historical perspective, allow this book to propose a new, seven-dimensional view of this phenomenon.

### List of References

Operations Outside the Russian Federation Was Adopted']. July 6. Available at: https:// www.interfax.ru/russia/850794.

.amazonaws.com/s3fs-public/publication/220601\_Jones\_Russia%27s\_Ill-Fated \_Invasion\_0.pdf?Ggqjb.JsRbJzr\_wlu5jrVT\_Xe3AW3jur.

['On the Integration of Means and Methods for Preparing Asymmetric Responses While Ensuring Military Security']. *Voennaya Mysl'* 1 (January): 48–60.

### List of Interviews24

Interview no. 1 Name: **Graeme P. Herd** Affiliation: George C. Marshall European Center for Security Studies Venue: Zoom Date: 12 January 2022 Time (Prague): 12:00–13:12

Interview no. 2 Name: **Nikolai Sokov** Affiliation: James Martin Center for Nonproliferation Studies & Vienna Center for Disarmament and Non-Proliferation Venue: Zoom Date: 13 January 2022 Time (Prague): 10:00–11:18

Interview no. 3 Name: **Simon Miles** Affiliation: Duke University Venue: Zoom Date: 17 January 2022 Time (Prague): 19:00–19:57

Interview no. 4 Name: **Stephen Blank** Affiliation: Foreign Policy Research Institute Venue: Skype Date: 17 January 2022 Time (Prague): 21:30–22:15

24 All interviewees gave their voluntary consent to be cited in this work.

Interview no. 5 Name: **Samuel Bendett** Affiliation: CNA Venue: Zoom Date: 19 January 2022 Time (Prague): 14:30–14:57

Interview no. 6 Name: **Iver B. Neumann** Affiliation: Fridtjof Nansen Institute Venue: Zoom Date: 19 January 2022 Time (Prague): 19:00–19:27

Interview no. 7 Name: **Mark Galeotti** Affiliation: UCL School of Slavonic and East European Studies, Royal United Services Institute (RUSI) & Mayak Intelligence Venue: Zoom Date: 26 January 2022 Time (Prague): 15:00–15:35

Interview no. 8 Name: **Dmitry Gorenburg** Affiliation: CNA Venue: Zoom Date: 31 January 2022 Time (Prague): 15:00–15:20

Interview no. 925 Name: **Vasily A. Veselov** Affiliation: Moscow State University Venue: Zoom Date: 03 February 2022 Time (Prague): 14:00–15:05

Interview no. 10 Name: **Scott Keefer** Affiliation: Bournemouth University Venue: Zoom Date: 23 February 2022 Time (Prague): 13:00–13:20

25 This conversation was not originally conducted in an interview format. It was a professional consultation as part of the author's remote internship pursued at that moment at Moscow State University. Having agreed to be cited in this text afterwards, Vasily A. Veselov is listed as an interviewee for consistency.


**6. Final-State Fermion Polarization** *Pf*

The polarization of a final-state fermion *Pf*=*μ*,*τ* can be expressed as the ratio between the difference of the cross sections for right and left handed final state helicities and their sum

$$P\_f = \frac{\sigma\_{\mathcal{R}\_f} - \sigma\_{\mathcal{L}\_f}}{\sigma\_{\mathcal{R}\_f} + \sigma\_{\mathcal{L}\_f}}.\tag{16}$$

In an experiment, it can be measured for the *τ*+*τ*− channel by reconstructing the *τ* polarization from the pion spectrum in the decay *τ* → *πν*. Details of the analysis of *Pτ* measurements at LEP are described in [13]. Computer programs TAOLA [26] and KORALZ [27,28] were applied for this analysis. Estimated improvement for *Pτ* and *τ* decay products over LEP time in ILC in the GigaZ program was done in [5].

In the case for unpolarized beams in the vicinity of the *Z* peak, the expression for channel *e*+*e*− → *τ*+*τ*− is simplified to

$$P\_{\tau}(\cos \theta\_{\tau}) \approx -\frac{A\_{\tau} + \frac{2 \cos \theta\_{\tau}}{1 + \cos^{2} \theta\_{\tau}} A\_{\ell}}{1 + \frac{2 \cos \theta\_{\tau}}{1 + \cos^{2} \theta\_{\tau}} A\_{\ell} A\_{\tau}}.\tag{17}$$

From this observable, one can extract information on the couplings *Aτ* and *Ae*, simultaneously.

In Figure 8 (left) we show the distribution of *Pτ* in the cosine of the scattering angle at the *Z* peak in the Born and 1-loop (weak, QED, and EW) approximations. The same conventions as in previous sections are applied for the shifts Δ*Pτ*. The shift due to pure QED RCs is approximately a constant close to zero. But one can see that this observable is very sensitive to the presence of weak-interaction corrections.

In the presence of initial beams polarization the expression depends on *P*eff:

$$P\_{\rm{\tau}}(\cos \theta) \approx -\frac{A\_{\rm{\tau}}(1 - A\_{\rm{\epsilon}}P\_{\rm{eff}}) + \frac{2\cos \theta\_{\rm{\tau}}}{(1 + \cos^{2} \theta\_{\rm{\tau}})}(A\_{\rm{\epsilon}} - P\_{\rm{eff}})}{(1 - A\_{\rm{\epsilon}}P\_{\rm{eff}}) + \frac{2\cos \theta\_{\rm{\tau}}}{(1 + \cos^{2} \theta\_{\rm{\tau}})}A\_{\rm{\tau}}(A\_{\rm{\epsilon}} - P\_{\rm{eff}})}.\tag{18}$$

which can be reduced to the short form neglecting the *AeAτ* and *AeP*eff terms:

$$P\_{\rm{T}}(\cos \theta\_{\rm{T}}) \approx -A\_{\rm{T}} - \frac{2 \cos \theta\_{\rm{T}}}{(1 + \cos^{2} \theta\_{\rm{T}})} (A\_{\rm{t}} - P\_{\rm{eff}}).\tag{19}$$

The influence of the initial particle polarization on *Pτ* at the *Z* peak is demonstrated in the Figure 8 (right). For comparison the unpolarized and two polarized cases (13) as functions of cos *ϑτ* are shown. It is seen that the behavior of *Pτ* depends on the polarization set choices very much, note that it even changes the sign for the *P*2 case. The corresponding shifts Δ*Pτ* also strongly depend on the initial beam polarization degrees and change the shape accordingly (note the maximum for *P*1).

In Figure 9 we show the dependence of *Pτ* on the c.m.s. energy in the Born and 1-loop approximations (weak, QED, and EW). We see that at energies above the *Z* resonance, both weak and QED radiative corrections to *Pτ* are large and considerable cancellations happen between their contributions. Note that theoretical uncertainties in weak and QED RCs are not correlated, so it is necessary to take into account higher-order effects to reduce the resulting uncertainty in the complete 1-loop result for *Pτ* at high energies.

**Figure 8.** (**Left**) The *Pτ* polarization in the Born and 1-loop (weak, pure QED, and EW) approximations as a function of cos *ϑτ* at √*s* = *MZ*. (**Right**) The *Pτ* polarization for unpolarized and polarized cases with (13) degrees of initial beam polarizations in the Born and EW 1-loop approximations vs. cosine of the final *τ* lepton scattering angle at the *Z* peak.

**Figure 9.** (**Left**) The *Pτ* polarization in the Born and 1-loop (weak, pure QED, and EW) approximations and Δ*Pτ* vs. c.m.s. energy in a wide range; (**Right**) the same for the *Z* peak region. The black dot indicates the value *Pτ* at the *Z* resonance.

In Figure 10 we show *Pτ* in the Born and 1-loop EW approximations for different sets of beam polarization degrees in a narrow bin around the *Z* resonance. The beam polarizations sets *P*1 and *P*2 are defined in Equation (13). One can see that the energy dependence of *Pτ* is strongly affected by a beam polarization choice outside the *Z* peak region. The same concerns the size of radiative corrections to *Pτ*, which are represented on the lower plot.

#### **Summary for** *Pτ*

The *Pτ* asymmetry is very sensitive to weak-interaction corrections and to the polarization degrees of the initial beams. Near the *Z* resonance the value of theoretical uncertainty of *Pτ* is determined by the interplay of uncertainties of rather large contributions pure QED and weak radiative corrections.

**Figure 10.** The *Pτ* polarization for (13) degrees of the initial beam polarizations in the Born and 1-loop EW approximations vs. c.m.s. energy in the *Z* peak region.

#### **7. Conclusions**

New opportunities of the future *e*+*e*− colliders: GigaZ options and new energy scale up to several TeV require modern tools for high-precision theoretical calculations of observables. We investigated *A*LR, *A*FB and *A*LRFB for *e*+*e*− → *μ*+*μ*− channel and polarization *Pτ* for the final state in *e*+*e*− → *τ*+*τ*− channel on the *Z* resonance and in the high energy region up to 500 GeV by using MCSANC. We evaluated the resulting shifts of asymmetries at the Born and EW levels of accuracy in different EW schemes. The numerical results presented above for pure QED, weak, and complete EW radiative corrections show an interplay between the weak and QED contributions to asymmetries. This fact indicates the necessity to consider those contributions always in combined way.

Asymmetries in *e*+*e*− annihilation processes provide a powerful tool for investigation of symmetries between three fermion generations. By studying all available asymmetries, one can extract parameters of weak interactions in the neutral current for all three charged leptons. So, by comparing the parameters it will be possible to verify the lepton universality hypothesis at a new level of precision.

Hypothetical extra neutral *Z* vector bosons [29] can contribute to the processes of *e*+*e*− annihilation. For example, effects of Kaluza–Klein excited vector bosons in the gauge Higgs unification on *e*+*e*− annihilation cross sections were considered in [30,31]. Since the new bosons can have couplings to left and right fermions being different from the SM ones, the asymmetries (especially with polarized beams) can help a lot in search for such *Z*bosons.

At the FCC-ee we have experimental precision tag in the sin2 *ϑ*eff *W* measurement of the order of 5 × 10−6, which means more than a thirty-fold improvement with respect to the current precision of 1.6 × 10−4. This is due to a factor of several hundred improvement on statistical errors and because of a considerable improvement in particle identification and vertexing. In order to provide theoretical predictions for the considered asymmetries with sufficiently small uncertainties which would not spoil the precision of the future experiments besides the complete 1-loop EW radiative corrections presented here we need:

Challenges in calculations of higher order QED effects for FCC-ee were discussed in Ref. [32]. The complete two-loop electroweak corrections in the vicinity of the *Z* boson peak have been presented in [33]. More details on challenges for high-precision theoretical calculations for future *e*+*e*− colliders can be found in [34,35].

**Author Contributions:** Conceptualization, A.A., S.B. and L.K.; methodology, A.A., S.B. and L.K.; software, A.A., S.B. and L.K.; validation, A.A., S.B. and L.K.; formal analysis, A.A., S.B. and L.K.; investigation, A.A., S.B. and L.K.; resources, A.A., S.B. and L.K.; data curation, A.A., S.B. and L.K.; writing—original draft preparation, A.A., S.B. and L.K.; writing—review and editing, A.A., S.B. and L.K. The authors claim to have contributed equally and significantly in this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by RFBR grant 20-02-00441.

**Acknowledgments:** The authors are grateful to Ya. Dydyshka, R. Sadykov, V. Yermolchyk, and A. Sapronov for fruitful discussions and numerical cross checks, and to A. Kalinovskaya for the help with preparation of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Abbreviations**

The following abbreviations are used in this manuscript: